module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Idempotents.Biproducts | {
"line": 79,
"column": 10
} | {
"line": 79,
"column": 21
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteBiproducts C\nn : ℕ\nF : Fin n → Karoubi C\n⊢ ∑ j, (Biproducts.bicone F).π j ≫ (Biproducts.bicone F).ι j = 𝟙 (Biproducts.bicone F).pt",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 522,
"column": 6
} | {
"line": 522,
"column": 78
} | [
{
"pp": "case refl.refl.refl\nC : Type u\ninst✝¹ : Groupoid C\nS : Subgroupoid C\nD : Type u_1\ninst✝ : Groupoid D\nφ : C ⥤ D\nhφ : Function.Injective φ.obj\nhφ' : im φ hφ = ⊤\nSn : S.IsNormal\nc : C\nγ : c ⟶ c\nγS : γ ∈ S.arrows c c\ncd' : φ.obj c = φ.obj c\nc' : C\nhb : φ.obj c = φ.obj c\nhb' : φ.obj c' = φ.o... | simp only [eqToHom_refl, Category.comp_id, Category.id_comp, inv_eq_inv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Chosen.End | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 15
} | [
{
"pp": "case left\nJ : Type u_1\nC : Type u_2\ninst✝² : Category.{v_1, u_2} C\ninst✝¹ : Category.{v_2, u_1} J\nF : Jᵒᵖ ⥤ J ⥤ C\ninst✝ : ChosenCoendsOfShape J C\nX : C\nf g : chosenCoend F ⟶ X\nh : ∀ (j : J), ι F j ≫ f = ι F j ≫ g\na : (multispanShapeCoend J).L\n⊢ (ChosenCoendsOfShape.cowedge F).ι.app (WalkingM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Constructions.WidePullbackOfTerminal | {
"line": 52,
"column": 45
} | {
"line": 52,
"column": 56
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nι : Type w\nB : C\nobjs : ι → C\narrows : (j : ι) → objs j ⟶ B\nc : Fan objs\nhc : IsLimit c\nhB : IsTerminal B\ns : WidePullbackCone arrows\nm : s.pt ⟶ (ofFan arrows c hB).pt\nx✝¹ : m ≫ (ofFan arrows c hB).base = s.base\nhm : ∀ (i : ι), m ≫ (ofFan arrows c hB).π ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Join.Basic | {
"line": 237,
"column": 28
} | {
"line": 237,
"column": 39
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nE' : Type u₄\ninst✝ : Category.{v₄, u₄} E'\nF : C ⥤ E\nG : D ⥤ E\nα : Prod.fst C D ⋙ F ⟶ Prod.snd C D ⋙ G\nx✝ y✝ : C\nf : x✝ ⟶ y✝\nd : D\n⊢ homInduction (fun x x_1 f ↦ F.map ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Join.Basic | {
"line": 239,
"column": 33
} | {
"line": 239,
"column": 44
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nE' : Type u₄\ninst✝ : Category.{v₄, u₄} E'\nF : C ⥤ E\nG : D ⥤ E\nα : Prod.fst C D ⋙ F ⟶ Prod.snd C D ⋙ G\nc : C\nd✝ y✝ : D\nf : d✝ ⟶ y✝\n⊢ homInduction (fun x x_1 f ↦ F.map ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Join.Basic | {
"line": 297,
"column": 21
} | {
"line": 297,
"column": 32
} | [
{
"pp": "case left\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nE' : Type u₄\ninst✝ : Category.{v₄, u₄} E'\nF F' : C ⋆ D ⥤ E\nαₗ : inclLeft C D ⋙ F ⟶ inclLeft C D ⋙ F'\nαᵣ : inclRight C D ⋙ F ⟶ inclRight C D ⋙ F'\nh :\n whiske... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Join.Basic | {
"line": 298,
"column": 22
} | {
"line": 298,
"column": 33
} | [
{
"pp": "case right\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nE' : Type u₄\ninst✝ : Category.{v₄, u₄} E'\nF F' : C ⋆ D ⥤ E\nαₗ : inclLeft C D ⋙ F ⟶ inclLeft C D ⋙ F'\nαᵣ : inclRight C D ⋙ F ⟶ inclRight C D ⋙ F'\nh :\n whisk... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Join.Basic | {
"line": 377,
"column": 38
} | {
"line": 377,
"column": 49
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nE' : Type u₄\ninst✝ : Category.{v₄, u₄} E'\nF G : C ⋆ D ⥤ E\neₗ : inclLeft C D ⋙ F ≅ inclLeft C D ⋙ G\neᵣ : inclRight C D ⋙ F ≅ inclRight C D ⋙ G\nh :\n whiskerRight (edgeTr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FormalCoproducts.Cech | {
"line": 78,
"column": 8
} | {
"line": 78,
"column": 19
} | [
{
"pp": "case h₂.h\nC : Type u\ninst✝¹ : Category.{v, u} C\nU : FormalCoproduct C\nα : Type\ninst✝ : HasProductsOfShape α C\ns : Fan fun x ↦ U\nφ : (i : s.pt.I) → s.pt.obj i ⟶ (U.powerFan α).pt.obj ((fun i a ↦ (s.proj a).f i) i)\ni : s.pt.I\na : α\nw✝ : ({ f := fun i a ↦ (s.proj a).f i, φ := φ } ≫ (U.powerFan α... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Preserves.BifunctorCokernel | {
"line": 100,
"column": 16
} | {
"line": 100,
"column": 27
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC : Type u_3\ninst✝¹¹ : Category.{v_1, u_1} C₁\ninst✝¹⁰ : Category.{v_2, u_2} C₂\ninst✝⁹ : Category.{v_3, u_3} C\ninst✝⁸ : HasZeroMorphisms C₁\ninst✝⁷ : HasZeroMorphisms C₂\ninst✝⁶ : HasZeroMorphisms C\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nc₁ : CokernelCofork f₁\nhc₁ : IsColimit c₁\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | {
"line": 80,
"column": 34
} | {
"line": 80,
"column": 45
} | [
{
"pp": "case h\nC : Type u\ninst✝ : Category.{v, u} C\nX Y : FormalCoproduct C\nf : X.I → Y.I\nF G : (i : X.I) → X.obj i ⟶ Y.obj (f i)\nh₂ : ∀ (i : X.I), { f := f, φ := F }.φ i ≫ eqToHom ⋯ = { f := f, φ := G }.φ i\ni : X.I\n⊢ F i = G i",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | {
"line": 297,
"column": 10
} | {
"line": 297,
"column": 21
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nA : Type u₁\ninst✝ : Category.{v₁, u₁} A\nX Y Z : FormalCoproduct C\nf : X ⟶ Z\ng : Y ⟶ Z\npb :\n (i : Function.Pullback f.f g.f) → PullbackCone (f.φ (↑i).1 ≫ eqToHom (@_proof_101 C inst✝¹ X Y Z f g i)) (g.φ (↑i).2)\nhpb : (i : Function.Pullback f.f g.f) → IsLim... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\n⊢ h.p₁ ≫ f₁ = h.p",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.as... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 185,
"column": 2
} | {
"line": 185,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\n⊢ h.p₃ ≫ f₃ = h.p",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.as... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 232,
"column": 50
} | {
"line": 232,
"column": 61
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝² : C\nx✝¹ x✝ : x✝² ⟶ h.pullback\nh₁ : x✝¹ ≫ h.p₁₂ = x✝ ≫ h.p₁₂\nh₂ : x✝¹ ≫ h.p₁₃ = x✝ ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 233,
"column": 10
} | {
"line": 233,
"column": 21
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝² : C\nx✝¹ x✝ : x✝² ⟶ h.pullback\nh₁ : x✝¹ ≫ h.p₁₂ = x✝ ≫ h.p₁₂\nh₂ : x✝¹ ≫ h.p₁₃ = x✝ ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 233,
"column": 40
} | {
"line": 233,
"column": 51
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝² : C\nx✝¹ x✝ : x✝² ⟶ h.pullback\nh₁ : x✝¹ ≫ h.p₁₂ = x✝ ≫ h.p₁₂\nh₂ : x✝¹ ≫ h.p₁₃ = x✝ ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 237,
"column": 24
} | {
"line": 237,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝ : C\na : x✝ ⟶ h₁₂.pullback\nb : x✝ ⟶ h₁₃.pullback\nw : a ≫ h₁₂.p₁ = b ≫ h₁₃.p₁\n⊢ (b ≫ h₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 241,
"column": 50
} | {
"line": 241,
"column": 61
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝² : C\nx✝¹ x✝ : x✝² ⟶ h.pullback\nh₁ : x✝¹ ≫ h.p₁₃ = x✝ ≫ h.p₁₃\nh₂ : x✝¹ ≫ h.p₂₃ = x✝ ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 242,
"column": 10
} | {
"line": 242,
"column": 21
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝² : C\nx✝¹ x✝ : x✝² ⟶ h.pullback\nh₁ : x✝¹ ≫ h.p₁₃ = x✝ ≫ h.p₁₃\nh₂ : x✝¹ ≫ h.p₂₃ = x✝ ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 242,
"column": 40
} | {
"line": 242,
"column": 51
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝² : C\nx✝¹ x✝ : x✝² ⟶ h.pullback\nh₁ : x✝¹ ≫ h.p₁₃ = x✝ ≫ h.p₁₃\nh₂ : x✝¹ ≫ h.p₂₃ = x✝ ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | {
"line": 246,
"column": 14
} | {
"line": 246,
"column": 25
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ S : C\nf₁ : X₁ ⟶ S\nf₂ : X₂ ⟶ S\nf₃ : X₃ ⟶ S\nh₁₂ : ChosenPullback f₁ f₂\nh₂₃ : ChosenPullback f₂ f₃\nh₁₃ : ChosenPullback f₁ f₃\nh : ChosenPullback₃ h₁₂ h₂₃ h₁₃\nx✝ : C\na : x✝ ⟶ h₁₃.pullback\nb : x✝ ⟶ h₂₃.pullback\nw : a ≫ h₁₃.p₂ = b ≫ h₂₃.p₂\n⊢ (b ≫ h₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 80,
"column": 12
} | {
"line": 80,
"column": 53
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\ns : Cone (cospan (𝟙 X) 0)\n⊢ ∀ (j : WalkingCospan), 0 ≫ (PullbackCone.mk 0 0 ⋯).π.app j = s.π.app j",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 82,
"column": 20
} | {
"line": 82,
"column": 31
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\ns : Cone (cospan (𝟙 X) 0)\n⊢ 0 ≫ PullbackCone.fst s = 𝟙 s.pt ≫ PullbackCone.fst s",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 179,
"column": 2
} | {
"line": 180,
"column": 20
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ IsPushout 0 0 coprod.inl coprod.inr",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
... | convert! @of_is_coproduct _ _ 0 X Y _ (colimit.isColimit _) HasZeroObject.zeroIsInitial
<;> subsingleton | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 179,
"column": 2
} | {
"line": 180,
"column": 20
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ IsPushout 0 0 coprod.inl coprod.inr",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
... | convert! @of_is_coproduct _ _ 0 X Y _ (colimit.isColimit _) HasZeroObject.zeroIsInitial
<;> subsingleton | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 179,
"column": 2
} | {
"line": 180,
"column": 20
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ IsPushout 0 0 coprod.inl coprod.inr",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
... | convert! @of_is_coproduct _ _ 0 X Y _ (colimit.isColimit _) HasZeroObject.zeroIsInitial
<;> subsingleton | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 192,
"column": 60
} | {
"line": 192,
"column": 71
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\ns : Cocone (span 0 (𝟙 X))\n⊢ PushoutCocone.inr s ≫ 0 = PushoutCocone.inr s ≫ 𝟙 s.pt",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Categor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 194,
"column": 12
} | {
"line": 194,
"column": 23
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\ns : Cocone (span 0 (𝟙 X))\nc : ∀ (j : WalkingSpan), s.ι.app j ≫ 0 = s.ι.app j ≫ 𝟙 s.pt\n⊢ ∀ (j : WalkingSpan), (PushoutCocone.mk 0 0 ⋯).ι.app j ≫ 0 = s.ι.app j",
"usedConstants": [
"Eq.mp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 46
} | [
{
"pp": "case h\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX Y : C\nb : BinaryBicone X Y\nh : b.IsBilimit\n⊢ IsPushout 0 b.inl 0 b.snd",
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Cate... | refine of_left ?_ (by simp) (of_isBilimit h) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.EquifiberedLimits | {
"line": 47,
"column": 8
} | {
"line": 47,
"column": 75
} | [
{
"pp": "J✝ : Type u_1\nK : Type u_2\nC : Type u_3\nD : Type u_4\nι : Type u_5\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : Category.{v_2, u_3} C\ninst✝³ : Category.{v_3, u_2} K\ninst✝² : Category.{v_4, u_4} D\nF : C ⥤ D\ninst✝¹ : ∀ (a b : C), HasCoproductsOfShape (a ⟶ b) D\nJ : Type u_1\ninst✝ : Category.{v_1, u... | simp [← NatTrans.naturality, ← NatTrans.comp_app, ← Over.comp_left] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.EquifiberedLimits | {
"line": 47,
"column": 8
} | {
"line": 47,
"column": 75
} | [
{
"pp": "J✝ : Type u_1\nK : Type u_2\nC : Type u_3\nD : Type u_4\nι : Type u_5\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : Category.{v_2, u_3} C\ninst✝³ : Category.{v_3, u_2} K\ninst✝² : Category.{v_4, u_4} D\nF : C ⥤ D\ninst✝¹ : ∀ (a b : C), HasCoproductsOfShape (a ⟶ b) D\nJ : Type u_1\ninst✝ : Category.{v_1, u... | simp [← NatTrans.naturality, ← NatTrans.comp_app, ← Over.comp_left] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.EquifiberedLimits | {
"line": 47,
"column": 8
} | {
"line": 47,
"column": 75
} | [
{
"pp": "J✝ : Type u_1\nK : Type u_2\nC : Type u_3\nD : Type u_4\nι : Type u_5\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : Category.{v_2, u_3} C\ninst✝³ : Category.{v_3, u_2} K\ninst✝² : Category.{v_4, u_4} D\nF : C ⥤ D\ninst✝¹ : ∀ (a b : C), HasCoproductsOfShape (a ⟶ b) D\nJ : Type u_1\ninst✝ : Category.{v_1, u... | simp [← NatTrans.naturality, ← NatTrans.comp_app, ← Over.comp_left] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.EquifiberedLimits | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 53
} | [
{
"pp": "case refine_1\nJ✝ : Type u_1\nK : Type u_2\nC : Type u_3\nD : Type u_4\nι : Type u_5\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : Category.{v_2, u_3} C\ninst✝³ : Category.{v_3, u_2} K\ninst✝² : Category.{v_4, u_4} D\nF : C ⥤ D\ninst✝¹ : ∀ (a b : C), HasCoproductsOfShape (a ⟶ b) D\nJ : Type u_1\ninst✝ : C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct | {
"line": 226,
"column": 4
} | {
"line": 226,
"column": 16
} | [
{
"pp": "case inst\nC : Type u_1\nM N : ℕ → C\ninst✝⁴ : Category.{v_1, u_1} C\nf : (n : ℕ) → M n ⟶ N n\ninst✝³ : HasCountableProducts C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasFiniteBiproducts C\ninst✝ : ∀ (n : ℕ), Epi (f n)\nn : ℕ\n⊢ ∀ (j : { x // x < n + 1 }),\n Epi (if h : ↑j < n then eqToHom ⋯ else if ... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct | {
"line": 226,
"column": 4
} | {
"line": 226,
"column": 16
} | [
{
"pp": "case inst\nC : Type u_1\nM N : ℕ → C\ninst✝⁴ : Category.{v_1, u_1} C\nf : (n : ℕ) → M n ⟶ N n\ninst✝³ : HasCountableProducts C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasFiniteBiproducts C\ninst✝ : ∀ (n : ℕ), Epi (f n)\nn : ℕ\n⊢ ∀ (j : { x // x < n + 1 }),\n Epi (if h : ↑j < n then eqToHom ⋯ else if ... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct | {
"line": 231,
"column": 4
} | {
"line": 231,
"column": 16
} | [
{
"pp": "case inst\nC : Type u_1\nM N : ℕ → C\ninst✝⁴ : Category.{v_1, u_1} C\nf : (n : ℕ) → M n ⟶ N n\ninst✝³ : HasCountableProducts C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasFiniteBiproducts C\ninst✝ : ∀ (n : ℕ), Epi (f n)\nn : ℕ\n⊢ ∀ (b : { x // ¬x < n + 1 }),\n IsIso (if h : ↑b < n then eqToHom ⋯ else ... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct | {
"line": 231,
"column": 4
} | {
"line": 231,
"column": 16
} | [
{
"pp": "case inst\nC : Type u_1\nM N : ℕ → C\ninst✝⁴ : Category.{v_1, u_1} C\nf : (n : ℕ) → M n ⟶ N n\ninst✝³ : HasCountableProducts C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasFiniteBiproducts C\ninst✝ : ∀ (n : ℕ), Epi (f n)\nn : ℕ\n⊢ ∀ (b : { x // ¬x < n + 1 }),\n IsIso (if h : ↑b < n then eqToHom ⋯ else ... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 59
} | [
{
"pp": "case w.h\nA : Type u₁\nB : Type u₂\nC : Type u₃\nA' : Type u₄\nB' : Type u₅\nC' : Type u₆\nA'' : Type u₇\nB'' : Type u₈\nC'' : Type u₉\ninst✝⁸ : Category.{v₁, u₁} A\ninst✝⁷ : Category.{v₂, u₂} B\ninst✝⁶ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\ninst✝⁵ : Category.{v₄, u₄} A'\ninst✝⁴ : Category.{v₅, u... | simp only [CatCommSq.vComp_iso_hom_app, Category.assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered | {
"line": 48,
"column": 29
} | {
"line": 48,
"column": 40
} | [
{
"pp": "J : Type u\ninst✝¹ : Category.{v, u} J\ninst✝ : IsFiltered J\nF : J ⥤ Type w₀\nx✝ y✝ x y : (j : J) × F.obj j\nf : x.fst ⟶ y.fst\nh : y.snd = (ConcreteCategory.hom (F.map f)) x.snd\n⊢ (ConcreteCategory.hom (F.map f)) x.snd = (ConcreteCategory.hom (F.map (𝟙 y.fst))) y.snd",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered | {
"line": 44,
"column": 4
} | {
"line": 59,
"column": 42
} | [
{
"pp": "case mp\nJ : Type u\ninst✝¹ : Category.{v, u} J\ninst✝ : IsFiltered J\nF : J ⥤ Type w₀\nx y : (j : J) × F.obj j\n⊢ Relation.EqvGen F.ColimitTypeRel x y →\n ∃ k f g, (ConcreteCategory.hom (F.map f)) x.snd = (ConcreteCategory.hom (F.map g)) y.snd",
"usedConstants": [
"Eq.mpr",
"Categor... | intro h
induction h with
| rel x y h =>
obtain ⟨f, h⟩ := h
exact ⟨y.1, f, 𝟙 _, by simpa using h.symm⟩
| refl x => exact ⟨x.1, 𝟙 _, 𝟙 _, rfl⟩
| symm _ _ _ h =>
obtain ⟨k, f, g, h⟩ := h
exact ⟨k, g, f, h.symm⟩
| trans x y z _ _ h h' =>
obtain ⟨k, f, g, h⟩ := h
ob... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered | {
"line": 44,
"column": 4
} | {
"line": 59,
"column": 42
} | [
{
"pp": "case mp\nJ : Type u\ninst✝¹ : Category.{v, u} J\ninst✝ : IsFiltered J\nF : J ⥤ Type w₀\nx y : (j : J) × F.obj j\n⊢ Relation.EqvGen F.ColimitTypeRel x y →\n ∃ k f g, (ConcreteCategory.hom (F.map f)) x.snd = (ConcreteCategory.hom (F.map g)) y.snd",
"usedConstants": [
"Eq.mpr",
"Categor... | intro h
induction h with
| rel x y h =>
obtain ⟨f, h⟩ := h
exact ⟨y.1, f, 𝟙 _, by simpa using h.symm⟩
| refl x => exact ⟨x.1, 𝟙 _, 𝟙 _, rfl⟩
| symm _ _ _ h =>
obtain ⟨k, f, g, h⟩ := h
exact ⟨k, g, f, h.symm⟩
| trans x y z _ _ h h' =>
obtain ⟨k, f, g, h⟩ := h
ob... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | {
"line": 207,
"column": 4
} | {
"line": 207,
"column": 59
} | [
{
"pp": "case w.h\nA : Type u₁\nB : Type u₂\nC : Type u₃\nA' : Type u₄\nB' : Type u₅\nC' : Type u₆\nA'' : Type u₇\nB'' : Type u₈\nC'' : Type u₉\ninst✝⁸ : Category.{v₁, u₁} A\ninst✝⁷ : Category.{v₂, u₂} B\ninst✝⁶ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\ninst✝⁵ : Category.{v₄, u₄} A'\ninst✝⁴ : Category.{v₅, u... | simp only [CatCommSq.vComp_iso_hom_app, Category.assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | {
"line": 238,
"column": 8
} | {
"line": 238,
"column": 19
} | [
{
"pp": "A : Type u₁\nB : Type u₂\nC : Type u₃\nA' : Type u₄\nB' : Type u₅\nC' : Type u₆\nA'' : Type u₇\nB'' : Type u₈\nC'' : Type u₉\ninst✝⁸ : Category.{v₁, u₁} A\ninst✝⁷ : Category.{v₂, u₂} B\ninst✝⁶ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\ninst✝⁵ : Category.{v₄, u₄} A'\ninst✝⁴ : Category.{v₅, u₅} B'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | {
"line": 242,
"column": 8
} | {
"line": 242,
"column": 19
} | [
{
"pp": "A : Type u₁\nB : Type u₂\nC : Type u₃\nA' : Type u₄\nB' : Type u₅\nC' : Type u₆\nA'' : Type u₇\nB'' : Type u₈\nC'' : Type u₉\ninst✝⁸ : Category.{v₁, u₁} A\ninst✝⁷ : Category.{v₂, u₂} B\ninst✝⁶ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\ninst✝⁵ : Category.{v₄, u₄} A'\ninst✝⁴ : Category.{v₅, u₅} B'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 13
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nH : Type u₃\ninst✝⁷ : Category.{v₁, u₁} C₁\ninst✝⁶ : Category.{v₂, u₂} C₂\ninst✝⁵ : Category.{v₃, u₃} H\nD₁ : Type u₄\nD₂ : Type u₅\ninst✝⁴ : Category.{v₄, u₄} D₁\ninst✝³ : Category.{v₅, u₅} D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived | {
"line": 104,
"column": 4
} | {
"line": 105,
"column": 73
} | [
{
"pp": "case mpr\nC₁ : Type u₁\nC₂ : Type u₂\nH : Type u₃\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} H\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nF : C₂ ⥤ H\ninst✝ : Φ.IsRightDerivabilityStructure\nhF : (Φ.functor ⋙ F).HasPoi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.BousfieldTransfiniteComposition | {
"line": 47,
"column": 28
} | {
"line": 47,
"column": 39
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nP : ObjectProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\nX Y : C\nf : X ⟶ Y\nx✝¹ : P.isLocal.transfiniteCompositionsOfShape J f\nZ : C\nhZ : P Z\nhf : P.isLocal.TransfiniteCompositionOfShape J f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.BousfieldTransfiniteComposition | {
"line": 55,
"column": 16
} | {
"line": 55,
"column": 51
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nP : ObjectProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\nX Y : C\nf : X ⟶ Y\nx✝² : P.isLocal.transfiniteCompositionsOfShape J f\nZ : C\nhZ : P Z\nhf : P.isLocal.TransfiniteCompositionOfShape J f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.BousfieldTransfiniteComposition | {
"line": 57,
"column": 15
} | {
"line": 57,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nP : ObjectProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\nX Y : C\nf : X ⟶ Y\nx✝ : P.isLocal.transfiniteCompositionsOfShape J f\nZ : C\nhZ : P Z\nhf : P.isLocal.TransfiniteCompositionOfShape J f\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 19
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} C₁\ninst✝² : Category.{v_2, u_2} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nρ : C₂ ⥤ C₁\ni : 𝟭 C₂ ⟶ ρ ⋙ Φ.functor\nhi : ∀ (X₂ : C₂), W₂ (i.app X₂)\nhW₁ : W₁ = W₂.inverseImage Φ.functor\ninst✝¹ : Φ.func... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.BousfieldTransfiniteComposition | {
"line": 64,
"column": 12
} | {
"line": 64,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nP : ObjectProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\nX Y : C\nf✝ : X ⟶ Y\nx✝² : P.isLocal.transfiniteCompositionsOfShape J f✝\nZ : C\nhZ : P Z\nhf : P.isLocal.TransfiniteCompositionOfShape J... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfLocalizedEquivalences | {
"line": 92,
"column": 42
} | {
"line": 104,
"column": 25
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD₁ : Type u_3\nD₂ : Type u_4\ninst✝¹¹ : Category.{v_1, u_1} C₁\ninst✝¹⁰ : Category.{v_2, u_2} C₂\ninst✝⁹ : Category.{v_3, u_3} D₁\ninst✝⁸ : Category.{v_4, u_4} D₂\nW₁ : MorphismProperty C₁\nW₁' : MorphismProperty D₁\nW₂ : MorphismProperty C₂\nW₂' : MorphismProperty D₂\nT :... | by
let ρ : B.LeftResolution (R.functor.obj X₂) := Classical.arbitrary _
exact ⟨{
X₁ := L.functor.objPreimage ρ.X₁
w :=
R.functor.preimage (iso.hom.app _ ≫
B.functor.map (L.functor.objObjPreimageIso ρ.X₁).hom ≫ ρ.w)
hw := by
simp only [← R.inverseImage_eq, Functor.comp... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | {
"line": 164,
"column": 29
} | {
"line": 164,
"column": 40
} | [
{
"pp": "A : Type u₁\nB : Type u₂\nC : Type u₃\ninst✝² : Category.{v₁, u₁} A\ninst✝¹ : Category.{v₂, u₂} B\ninst✝ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\nx y : F ⊡ G\neₗ : x.fst ≅ y.fst\neᵣ : x.snd ≅ y.snd\nw : F.map eₗ.hom ≫ y.iso.hom = x.iso.hom ≫ G.map eᵣ.hom\n⊢ F.map eₗ.inv ≫ x.iso.hom = y.iso.hom ≫ G.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | {
"line": 298,
"column": 4
} | {
"line": 298,
"column": 62
} | [
{
"pp": "case w.h\nA : Type u₁\nB : Type u₂\nC : Type u₃\ninst✝³ : Category.{v₁, u₁} A\ninst✝² : Category.{v₂, u₂} B\ninst✝¹ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\nX : Type u₄\ninst✝ : Category.{v₄, u₄} X\nS S' : CatCommSqOver F G X\neₗ : S.fst ≅ S'.fst\neᵣ : S.snd ≅ S'.snd\nw : whiskerRight eₗ.hom F ≫ S'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | {
"line": 385,
"column": 10
} | {
"line": 385,
"column": 21
} | [
{
"pp": "A : Type u₁\nB : Type u₂\nC : Type u₃\ninst✝³ : Category.{v₁, u₁} A\ninst✝² : Category.{v₂, u₂} B\ninst✝¹ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\nX : Type u₄\ninst✝ : Category.{v₄, u₄} X\nJ K : X ⥤ F ⊡ G\ne₁ : J ⋙ π₁ F G ≅ K ⋙ π₁ F G\ne₂ : J ⋙ π₂ F G ≅ K ⋙ π₂ F G\ncoh :\n whiskerRight e₁.hom F ≫\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | {
"line": 420,
"column": 10
} | {
"line": 420,
"column": 53
} | [
{
"pp": "A : Type u₁\nB : Type u₂\nC : Type u₃\ninst✝³ : Category.{v₁, u₁} A\ninst✝² : Category.{v₂, u₂} B\ninst✝¹ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\nX : Type u₄\ninst✝ : Category.{v₄, u₄} X\nJ K : X ⥤ F ⊡ G\ne₁ : J ⋙ π₁ F G ≅ K ⋙ π₁ F G\ne₂ : J ⋙ π₂ F G ≅ K ⋙ π₂ F G\ncoh :\n autoParam\n (whiskerR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | {
"line": 438,
"column": 12
} | {
"line": 438,
"column": 55
} | [
{
"pp": "A : Type u₁\nB : Type u₂\nC : Type u₃\ninst✝³ : Category.{v₁, u₁} A\ninst✝² : Category.{v₂, u₂} B\ninst✝¹ : Category.{v₃, u₃} C\nF : A ⥤ B\nG : C ⥤ B\nX : Type u₄\ninst✝ : Category.{v₄, u₄} X\nJ K : X ⥤ F ⊡ G\ne₁ : J ⋙ π₁ F G ≅ K ⋙ π₁ F G\ne₂ : J ⋙ π₂ F G ≅ K ⋙ π₂ F G\ncoh :\n autoParam\n (whiskerR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Monoidal.Braided | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 15
} | [
{
"pp": "case refine_1\nC : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝³ : MonoidalCategory C\ninst✝² : W.IsMonoidal\ninst✝¹ : L.IsLocalization W\nunit : D\nε : L.obj (𝟙_ C) ≅ unit\ninst✝ : BraidedCategory C\n⊢ failed to prett... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Monoidal.Braided | {
"line": 123,
"column": 4
} | {
"line": 123,
"column": 15
} | [
{
"pp": "case refine_2\nC : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝³ : MonoidalCategory C\ninst✝² : W.IsMonoidal\ninst✝¹ : L.IsLocalization W\nunit : D\nε : L.obj (𝟙_ C) ≅ unit\ninst✝ : BraidedCategory C\n⊢ failed to prett... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.CategoryTheory.Coherence | {
"line": 219,
"column": 2
} | {
"line": 219,
"column": 13
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : C\nf g : X ⟶ Y\nw : f ≫ 𝟙 Y = g\n⊢ f = g",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.CategoryTheory.Coherence | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 13
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : C\nf g : X ⟶ Y\nw : f = g ≫ 𝟙 Y\n⊢ f = g",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Free.Basic | {
"line": 375,
"column": 8
} | {
"line": 375,
"column": 23
} | [
{
"pp": "case f\nC : Type u\nD : Type u'\ninst✝¹ : Category.{v', u'} D\ninst✝ : MonoidalCategory D\nf : C → D\nX✝ Y✝ x✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\na✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representa... | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Monoidal.Free.Basic | {
"line": 378,
"column": 8
} | {
"line": 378,
"column": 23
} | [
{
"pp": "case f\nC : Type u\nD : Type u'\ninst✝¹ : Category.{v', u'} D\ninst✝ : MonoidalCategory D\nf : C → D\nX✝ Y✝ x✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\na✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representa... | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Monad.EquivMon | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nM : Mon (C ⥤ C)\nX : C\n⊢ M.X.map (μ.app X) ≫ μ.app X = μ.app (M.X.obj X) ≫ μ.app X",
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Categor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.EquivMon | {
"line": 69,
"column": 4
} | {
"line": 69,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nM : Mon (C ⥤ C)\nX : C\n⊢ η.app (M.X.obj X) ≫ μ.app X = 𝟙 ((𝟭 C).obj (M.X.obj X))",
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Categor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.EquivMon | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nM : Mon (C ⥤ C)\nX : C\n⊢ M.X.map (η.app X) ≫ μ.app X = 𝟙 (M.X.obj ((𝟭 C).obj X))",
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Categor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.EquivMon | {
"line": 88,
"column": 8
} | {
"line": 88,
"column": 39
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX✝ Y : Mon (C ⥤ C)\nf : X✝ ⟶ Y\nX : C\n⊢ (ofMon X✝).η.app X ≫ f.hom.app X = (ofMon Y).η.app X",
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mon.Hom.hom",
"Ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.EquivMon | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 39
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : Mon (C ⥤ C)\nf : X ⟶ Y\nZ : C\n⊢ (ofMon X).μ.app Z ≫ f.hom.app Z = ((ofMon X).map (f.hom.app Z) ≫ f.hom.app ((ofMon Y).obj Z)) ≫ (ofMon Y).μ.app Z",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.LocallyCartesianClosed.Over | {
"line": 92,
"column": 42
} | {
"line": 92,
"column": 53
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : ChosenPullbacks C\nX : C\nY : Over X\nm : Y ⟶ Over.mk (𝟙 X)\n⊢ Over.Hom.left m = Over.Hom.left ((fun Y ↦ Over.homMk Y.hom ⋯) Y)",
"usedConstants": [
"CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOver._proof_2",
"Categor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 58
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalLeftAction C D\ninst✝¹ : MonoidalLeftAction C D'\ninst✝ : F.LaxLeftLinear C\nc c' : C\nd : D\n⊢ c ⊴ₗ μₗ F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 29
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalLeftAction C D\ninst✝¹ : MonoidalLeftAction C D'\ninst✝ : F.LaxLeftLinear C\nd : D\n⊢ (λₗ (F.obj d)).inv ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 58
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalLeftAction C D\ninst✝¹ : MonoidalLeftAction C D'\ninst✝ : F.OplaxLeftLinear C\nc c' : C\nd : D\n⊢ δₗ F c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 33
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalLeftAction C D\ninst✝¹ : MonoidalLeftAction C D'\ninst✝ : F.OplaxLeftLinear C\nd : D\n⊢ δₗ F (𝟙_ C) d ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 244,
"column": 2
} | {
"line": 244,
"column": 58
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalRightAction C D\ninst✝¹ : MonoidalRightAction C D'\ninst✝ : F.LaxRightLinear C\nd : D\nc c' : C\n⊢ μᵣ F d... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 29
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalRightAction C D\ninst✝¹ : MonoidalRightAction C D'\ninst✝ : F.LaxRightLinear C\nd : D\n⊢ (ρᵣ (F.obj d)).i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 58
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalRightAction C D\ninst✝¹ : MonoidalRightAction C D'\ninst✝ : F.OplaxRightLinear C\nd : D\nc c' : C\n⊢ δᵣ F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {
"line": 309,
"column": 2
} | {
"line": 309,
"column": 33
} | [
{
"pp": "D : Type u_1\nD' : Type u_2\ninst✝⁶ : Category.{v_1, u_1} D\ninst✝⁵ : Category.{v_2, u_2} D'\nF : D ⥤ D'\nC : Type u_3\ninst✝⁴ : Category.{v_3, u_3} C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalRightAction C D\ninst✝¹ : MonoidalRightAction C D'\ninst✝ : F.OplaxRightLinear C\nd : D\n⊢ δᵣ F d (𝟙_ C)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 76,
"column": 4
} | {
"line": 76,
"column": 39
} | [
{
"pp": "case w.h\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nc₁ c₂ c₃ : C\nd : D\n⊢ ((mopEquiv (D ⥤ D)).inverse.map\n (Quiver.Hom.mop { app := fun x ↦ (αₗ c₁ c₂ x).inv, naturality := ⋯ } ▷ (cu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 39
} | [
{
"pp": "case h.w.h\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nx : C\nt : D\n⊢ (λ_ ((curriedActionMop C D).obj x)).inv.unmop.app t =\n ((curriedActionMop C D).map (λ_ x).inv ≫\n Quiver.Ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 82,
"column": 4
} | {
"line": 82,
"column": 40
} | [
{
"pp": "case h.w.h\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nx : C\nt : D\n⊢ (ρ_ ((curriedActionMop C D).obj x)).inv.unmop.app t =\n ((curriedActionMop C D).map (ρ_ x).inv ≫\n Quiver.Ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 39
} | [
{
"pp": "case w.h\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nc₁ c₂ c₃ : C\nd : D\n⊢ ({ app := fun x ↦ (αᵣ x c₁ c₂).inv, naturality := ⋯ } ▷ (curriedAction C D).obj c₃ ≫\n { app := fun x ↦ (αᵣ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 180,
"column": 4
} | {
"line": 180,
"column": 39
} | [
{
"pp": "case w.h\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nx : C\nt : D\n⊢ (λ_ ((curriedAction C D).obj x)).inv.app t =\n ((curriedAction C D).map (λ_ x).inv ≫\n { app := fun x_1 ↦ (αᵣ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 40
} | [
{
"pp": "case w.h\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nx : C\nt : D\n⊢ (ρ_ ((curriedAction C D).obj x)).inv.app t =\n ((curriedAction C D).map (ρ_ x).inv ≫\n { app := fun x_1 ↦ (αᵣ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalLeftAction C D\nx y : C\nf : x ≅ y\nz : D\n⊢ f.hom ⊵ₗ z ≫ f.inv ⊵ₗ z = 𝟙 (x ⊙ₗ z)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MonoidalCategory.Mon... | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalLeftAction C D\nx y : C\nf : x ≅ y\nz : D\n⊢ f.hom ⊵ₗ z ≫ f.inv ⊵ₗ z = 𝟙 (x ⊙ₗ z)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MonoidalCategory.Mon... | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalLeftAction C D\nx y : C\nf : x ≅ y\nz : D\n⊢ f.hom ⊵ₗ z ≫ f.inv ⊵ₗ z = 𝟙 (x ⊙ₗ z)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MonoidalCategory.Mon... | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalRightAction C D\nx y : D\nf : x ≅ y\nz : C\n⊢ f.hom ⊵ᵣ z ≫ f.inv ⊵ᵣ z = 𝟙 (x ⊙ᵣ z)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQu... | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalRightAction C D\nx y : D\nf : x ≅ y\nz : C\n⊢ f.hom ⊵ᵣ z ≫ f.inv ⊵ᵣ z = 𝟙 (x ⊙ᵣ z)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQu... | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalRightAction C D\nx y : D\nf : x ≅ y\nz : C\n⊢ f.hom ⊵ᵣ z ≫ f.inv ⊵ᵣ z = 𝟙 (x ⊙ᵣ z)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQu... | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 61,
"column": 4
} | {
"line": 62,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction Cᴹᵒᵖ D\nc₁ c₂ c₃ : C\nd : D\n⊢ d ⊴ᵣ (α_ c₁ c₂ c₃).hom.mop ≫\n (αᵣ d { unmop := c₂ ⊗ c₃ } { unmop := c₁ }).hom ≫ (αᵣ d { unmop := c₃ } { unmop := c₂ }... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 86,
"column": 4
} | {
"line": 87,
"column": 61
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nc₁ c₂ c₃ : Cᴹᵒᵖ\nd : D\n⊢ d ⊴ᵣ (α_ c₁ c₂ c₃).hom.unmop ≫ (αᵣ d (c₂ ⊗ c₃).unmop c₁.unmop).hom ≫ (αᵣ d c₃.unmop c₂.unmop).hom ⊵ᵣ c₁.unmop =\n (αᵣ d ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 133,
"column": 8
} | {
"line": 133,
"column": 56
} | [
{
"pp": "case a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nc✝ c'✝ : Cᵒᵖ\nd✝ d'✝ : Dᵒᵖ\nf : unop c'✝ ⟶ unop c✝\ng : unop d'✝ ⟶ unop d✝\n⊢ (Quiver.Hom.unop (op f) ⊙ₗₘ Quiver.Hom.unop (op g)).op.unop =\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 52
} | [
{
"pp": "case a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction Cᵒᵖ Dᵒᵖ\nc✝ c'✝ : C\nd✝ d'✝ : D\nf : c✝ ⟶ c'✝\ng : d✝ ⟶ d'✝\n⊢ (f.op ⊙ₗₘ g.op).unop.op = ((f.op ⊵ₗ op d✝).unop ≫ (op c'✝ ⊴ₗ g.op).unop).op",
"u... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 275,
"column": 4
} | {
"line": 276,
"column": 59
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction Cᴹᵒᵖ D\nc₁ c₂ c₃ : C\nd : D\n⊢ (α_ c₁ c₂ c₃).hom.mop ⊵ₗ d ≫\n (αₗ { unmop := c₂ ⊗ c₃ } { unmop := c₁ } d).hom ≫\n (αₗ { unmop := c₃ } { unmop :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 298,
"column": 4
} | {
"line": 299,
"column": 59
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nc₁ c₂ c₃ : Cᴹᵒᵖ\nd : D\n⊢ (α_ c₁ c₂ c₃).hom.unmop ⊵ₗ d ≫ (αₗ (c₂ ⊗ c₃).unmop c₁.unmop d).hom ≫ (αₗ c₃.unmop c₂.unmop (c₁.unmop ⊙ₗ d)).hom =\n (αₗ c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 345,
"column": 8
} | {
"line": 345,
"column": 57
} | [
{
"pp": "case a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nc✝ c'✝ : Cᵒᵖ\nd✝ d'✝ : Dᵒᵖ\nf : unop d'✝ ⟶ unop d✝\ng : unop c'✝ ⟶ unop c✝\n⊢ (Quiver.Hom.unop (op f) ⊙ᵣₘ Quiver.Hom.unop (op g)).op.unop =\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 386,
"column": 4
} | {
"line": 386,
"column": 53
} | [
{
"pp": "case a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction Cᵒᵖ Dᵒᵖ\nc✝ c'✝ : C\nd✝ d'✝ : D\nf : d✝ ⟶ d'✝\ng : c✝ ⟶ c'✝\n⊢ (f.op ⊙ᵣₘ g.op).unop.op = ((f.op ⊵ᵣ op c✝).unop ≫ (op d'✝ ⊴ᵣ g.op).unop).op",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp_ | {
"line": 48,
"column": 6
} | {
"line": 48,
"column": 17
} | [
{
"pp": "case h\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nX : C\nG : CommGrp C\nH I : (Grp C)ᵒᵖ\nf : H ⟶ I\ng h : unop H ⟶ G.toGrp\n⊢ (f.unop ≫ (g * h)).hom.hom = (f.unop ≫ g * f.unop ≫ h).hom.hom",
"usedConstants": [
"CategoryTheory.Comm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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