module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 164,
"column": 48
} | {
"line": 164,
"column": 50
} | {
"line": 164,
"column": 51
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn✝ : ℕ\ninst✝ : Group G\nA : Rep k G\nn : ℕ\nf : (Fin n → G) → ↑A\nh : (ConcreteCategory.hom (d A n)) f = 0\n⊢ (ComplexShape.up ℕ).next n = n + 1",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Nat.instOne",
"congrArg",
"AddRig... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 164,
"column": 58
} | {
"line": 164,
"column": 60
} | {
"line": 164,
"column": 61
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn✝ : ℕ\ninst✝ : Group G\nA : Rep k G\nn : ℕ\nf : (Fin n → G) → ↑A\nh : (ConcreteCategory.hom (d A n)) f = 0\n⊢ (ConcreteCategory.hom ((forget₂ (ModuleCat k) Ab).map ((inhomogeneousCochains A).d n (n + 1)))) f = 0",
"ppTerm": "?m.43",
"assigned": true,
"use... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 178,
"column": 65
} | {
"line": 178,
"column": 67
} | {
"line": 178,
"column": 68
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nn : ℕ\nf : (Fin n → G) → ↑A\nh : (ConcreteCategory.hom (d A n)) f = 0\n⊢ (ComplexShape.up ℕ).next n = n + 1",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Nat.instOne",
"congrArg",
"AddRightCancel... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 178,
"column": 75
} | {
"line": 178,
"column": 77
} | {
"line": 178,
"column": 78
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nn : ℕ\nf : (Fin n → G) → ↑A\nh : (ConcreteCategory.hom (d A n)) f = 0\n⊢ (ConcreteCategory.hom ((forget₂ (ModuleCat k) Ab).map ((inhomogeneousCochains A).d n (n + 1)))) f = 0",
"ppTerm": "?m.48",
"assigned": true,
"usedConstan... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 177,
"column": 42
} | {
"line": 177,
"column": 44
} | {
"line": 178,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nn : ℕ\nf : (Fin n → G) → ↑A\nh : (ConcreteCategory.hom (d A n)) f = 0\n⊢ (ConcreteCategory.hom (iCocycles A n)) (cocyclesMk f h) = f",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPre... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 199,
"column": 51
} | {
"line": 199,
"column": 53
} | {
"line": 200,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nn : ℕ\nC : ↑(groupCohomology A n) → Prop\nx : ↑(groupCohomology A n)\nh : ∀ (x : ↑(cocycles A n)), C ((ConcreteCategory.hom (π A n)) x)\n⊢ C x",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"CategoryTheory.Epi... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 148,
"column": 74
} | {
"line": 148,
"column": 76
} | {
"line": 148,
"column": 77
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type v'\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA✝ : Rep k G\nB✝ : Rep k H\nA : Rep k G\nB : Rep k H\nf : A ⟶ res φ B\ng : H\n⊢ Coinvariants.lift (tprod (MonoidHom.comp (Representation.leftRegular k H) φ) A.ρ)\n (TensorProduct.lift\n ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 149,
"column": 16
} | {
"line": 149,
"column": 18
} | {
"line": 150,
"column": 4
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type v'\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA✝ : Rep k G\nB✝ : Rep k H\nA : Rep k G\nB : Rep k H\nf : ind φ A ⟶ B\n⊢ (fun f ↦\n ofHom\n {\n toLinearMap :=\n Coinvariants.lift (tprod (MonoidHom.comp (Rep... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 152,
"column": 17
} | {
"line": 152,
"column": 19
} | {
"line": 152,
"column": 20
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type v'\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA✝ : Rep k G\nB✝ : Rep k H\nA : Rep k G\nB : Rep k H\nx✝ : A ⟶ res φ B\n⊢ (fun f ↦ ofHom { toLinearMap := (Hom.hom f).toLinearMap ∘ₗ IndV.mk φ A.ρ 1, isIntertwining' := ⋯ })\n ((fun f ↦\n ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 160,
"column": 41
} | {
"line": 160,
"column": 43
} | {
"line": 161,
"column": 6
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type v'\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nX'✝ X✝ : Rep k G\nY✝ : Rep k H\nx✝¹ : X'✝ ⟶ X✝\nx✝ : X✝ ⟶ (resFunctor φ).obj Y✝\n⊢ (indResHomEquiv φ X'✝ Y✝).toEquiv.symm (x✝¹ ≫ x✝) =\n (indFunctor k φ).map x✝¹ ≫ (indR... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 163,
"column": 33
} | {
"line": 163,
"column": 35
} | {
"line": 163,
"column": 36
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type v'\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\n⊢ ∀ {X : Rep k G} {Y Y' : Rep k H} (f : (indFunctor k φ).obj X ⟶ Y) (g : Y ⟶ Y'),\n (indResHomEquiv φ X Y').toEquiv (f ≫ g) = (indResHomEquiv φ X Y).toEquiv f ≫ (resFunc... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 193,
"column": 14
} | {
"line": 193,
"column": 16
} | {
"line": 193,
"column": 17
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ng : G\n⊢ TensorProduct.lift\n (((lift (↑A →ₗ[k] ↑B →ₗ[k] (((MonoidalCategory.curr... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 194,
"column": 53
} | {
"line": 194,
"column": 55
} | {
"line": 195,
"column": 4
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nx✝ : H\n⊢ TensorProduct.lift\n (Coinvariants.lift (tprod (MonoidHom.comp (Represe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 205,
"column": 46
} | {
"line": 205,
"column": 48
} | {
"line": 206,
"column": 2
} | [
{
"pp": "k : Type u\ninst✝² : CommRing k\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nh : H\nx : ↑A\ny : ↑B\n⊢ (ConcreteCategory.hom (coinvariantsTensorIndHom φ A B))\n ((((ind φ A).coinvariantsTensorMk B) ((IndV.mk φ A.ρ h) x)) y) =\n ((A.coinvariantsTensorMk ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 222,
"column": 78
} | {
"line": 222,
"column": 80
} | {
"line": 223,
"column": 6
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ns : G\nx : ↑A\ny : ↑B\n⊢ (((Representation.ind φ A.ρ).tprod B.ρ) (φ s)) ((IndV.mk φ A.ρ ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 218,
"column": 4
} | {
"line": 223,
"column": 39
} | {
"line": 225,
"column": 0
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ns : G\n⊢ TensorProduct.lift ((ind φ A).coinvariantsTensorMk B ∘ₗ IndV.mk φ A.ρ 1) ∘ₗ\n ... | [] | simp only [MonoidalCategory.curriedTensor_obj_obj, tensor_V, tensor_ρ, tprod_apply,
MonoidHom.coe_comp, Function.comp_apply]
ext x y
simpa [Coinvariants.mk_eq_iff, coinvariantsTensorMk] using
Coinvariants.mem_ker_of_eq (φ s) (IndV.mk φ A.ρ (1 : H) x ⊗ₜ[k] y) _ <| by
simp [← Coinvariants.mk_inv... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RepresentationTheory.Induced | {
"line": 218,
"column": 4
} | {
"line": 223,
"column": 39
} | {
"line": 225,
"column": 0
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ns : G\n⊢ TensorProduct.lift ((ind φ A).coinvariantsTensorMk B ∘ₗ IndV.mk φ A.ρ 1) ∘ₗ\n ... | [] | simp only [MonoidalCategory.curriedTensor_obj_obj, tensor_V, tensor_ρ, tprod_apply,
MonoidHom.coe_comp, Function.comp_apply]
ext x y
simpa [Coinvariants.mk_eq_iff, coinvariantsTensorMk] using
Coinvariants.mem_ker_of_eq (φ s) (IndV.mk φ A.ρ (1 : H) x ⊗ₜ[k] y) _ <| by
simp [← Coinvariants.mk_inv... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RepresentationTheory.Induced | {
"line": 217,
"column": 74
} | {
"line": 217,
"column": 76
} | {
"line": 218,
"column": 4
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ns : G\n⊢ TensorProduct.lift ((ind φ A).coinvariantsTensorMk B ∘ₗ IndV.mk φ A.ρ 1) ∘ₗ\n ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 231,
"column": 54
} | {
"line": 231,
"column": 56
} | {
"line": 232,
"column": 2
} | [
{
"pp": "k : Type u\ninst✝² : CommRing k\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nx : ↑A\ny : ↑B\n⊢ (ConcreteCategory.hom (coinvariantsTensorIndInv φ A B)) ((Coinvariants.mk (A.ρ.tprod (res φ B).ρ)) (x ⊗ₜ[k] y)) =\n (((ind φ A).coinvariantsTensorMk B) ((IndV.mk ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 249,
"column": 68
} | {
"line": 249,
"column": 70
} | {
"line": 249,
"column": 71
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nh : H\na : ↑A\nb : ↑B\n⊢ (((Representation.ind φ A.ρ).tprod B.ρ) h) ((IndV.mk φ A.ρ h) a... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 245,
"column": 16
} | {
"line": 245,
"column": 18
} | {
"line": 246,
"column": 4
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\n⊢ coinvariantsTensorIndHom φ A B ≫ coinvariantsTensorIndInv φ A B = 𝟙 (((coinvariantsTe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 250,
"column": 16
} | {
"line": 250,
"column": 18
} | {
"line": 251,
"column": 4
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\n⊢ coinvariantsTensorIndInv φ A B ≫ coinvariantsTensorIndHom φ A B = 𝟙 (((coinvariantsTe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Induced | {
"line": 261,
"column": 79
} | {
"line": 261,
"column": 81
} | {
"line": 262,
"column": 4
} | [
{
"pp": "k : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nX Y : Rep k H\nf : X ⟶ Y\n⊢ ((coinvariantsTensor k H).obj (ind φ A)).map f ≫ (coinvarian... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 60,
"column": 91
} | {
"line": 60,
"column": 93
} | {
"line": 61,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\n⊢ ∀ (i j : ℕ),\n (ComplexShape.up ℕ).Rel i j →\n A.leftRegularHomEquiv.toModuleIso.hom ≫ (moduleCatCochainComplex A g).d i j =\n ((resolution k g hg).co... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 74,
"column": 54
} | {
"line": 74,
"column": 56
} | {
"line": 74,
"column": 57
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\n⊢ A.ρ.invariants = (Hom.hom (A.applyAsHom g - 𝟙 A)).ker",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 84,
"column": 75
} | {
"line": 84,
"column": 77
} | {
"line": 84,
"column": 78
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nh₀ : NeZero i\nhi : Even i\n⊢ ModuleCat.ofHom (Hom.hom (A.applyAsHom g - 𝟙 A)).toLinearMap ≫ ModuleCat.ofHom (Hom.hom A.norm).toLinearMap = 0",
"ppTerm": "... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 85,
"column": 5
} | {
"line": 85,
"column": 7
} | {
"line": 85,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nh₀ : NeZero i\nhi : Even i\n⊢ ModuleCat.ofHom (Hom.hom A.norm).toLinearMap ≫ ModuleCat.ofHom (Hom.hom (A.applyAsHom g - 𝟙 A)).toLinearMap = 0",
"ppTerm": "... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 85,
"column": 30
} | {
"line": 85,
"column": 32
} | {
"line": 85,
"column": 33
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nh₀ : NeZero i\nhi : Even i\n⊢ ∀ (i j : ℕ), (ComplexShape.up ℕ).Rel i j → Odd (i + j)",
"ppTerm": "?m.129",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 86,
"column": 5
} | {
"line": 86,
"column": 7
} | {
"line": 86,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nh₀ : NeZero i\nhi : Even i\n⊢ (ComplexShape.up ℕ).Rel ((ComplexShape.up ℕ).prev i) i",
"ppTerm": "?m.130",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 87,
"column": 5
} | {
"line": 87,
"column": 7
} | {
"line": 87,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nh₀ : NeZero i\nhi : Even i\n⊢ (ComplexShape.up ℕ).Rel i ((ComplexShape.up ℕ).next i)",
"ppTerm": "?m.155",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 100,
"column": 93
} | {
"line": 100,
"column": 95
} | {
"line": 101,
"column": 2
} | [
{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
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} | {
"line": 119,
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{
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"Nat.instOne",... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
"line": 133,
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
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} | {
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{
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"usedConsta... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
"line": 124,
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} | {
"line": 125,
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{
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"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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} | {
"line": 117,
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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} | {
"line": 137,
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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} | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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{
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"_private.Mathlib.RepresentationTheory.Homological.Resolution.0.Rep.standardComplex.x_... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
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} | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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} | {
"line": 226,
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} | {
"line": 227,
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 264,
"column": 67
} | {
"line": 264,
"column": 69
} | {
"line": 264,
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 272,
"column": 87
} | {
"line": 272,
"column": 89
} | {
"line": 273,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Monoid G\n⊢ (forget₂ToModuleCatHomotopyEquiv k G).hom.f 0 = (forget₂ (Rep k G) (ModuleCat k)).map (ε k G)",
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"usedConstants": [
"HomologicalComplex.eqToHom_f",
"Finsupp.instFunLike",
"OrderHom.i... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 285,
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} | {
"line": 285,
"column": 67
} | {
"line": 286,
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} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Monoid G\nx✝ : ↑((standardComplex k G).X 1)\n⊢ (forget₂ToModuleCat k G).d 1 0 ≫ (forget₂ (Rep k G) (ModuleCat k)).map (ε k G) = 0",
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"usedConstants": [
"Eq.mpr",
"Rep.V",
"ChainComplex",
... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 282,
"column": 62
} | {
"line": 282,
"column": 64
} | {
"line": 283,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Monoid G\n⊢ (standardComplex k G).d 1 0 ≫ ε k G = 0",
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"usedConstants": [
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"ChainComplex",
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Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 301,
"column": 51
} | {
"line": 301,
"column": 53
} | {
"line": 302,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Monoid G\n⊢ ((forget₂ (Rep k G) (ModuleCat k)).mapHomologicalComplex (ComplexShape.down ℕ)).map (εToSingle₀ k G) ≫\n (HomologicalComplex.singleMapHomologicalComplex (forget₂ (Rep k G) (ModuleCat k)) (ComplexShape.down ℕ) 0).hom.app\n (trivial k G k... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
"line": 148,
"column": 7
} | {
"line": 148,
"column": 9
} | {
"line": 148,
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{
"pp": "K L : Type\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : FiniteDimensional K L\ninst✝¹ : IsGalois K L\ninst✝ : IsCyclic Gal(L/K)\ng : Gal(L/K)\nhg : ∀ (x : Gal(L/K)), x ∈ Subgroup.zpowers g\nx✝ : L\nhx✝ : (Algebra.norm K) x✝ = 1\nx : L\nhx : (Algebra.norm K) x = 1\nxu : Lˣ := ⋯.un... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 307,
"column": 95
} | {
"line": 307,
"column": 97
} | {
"line": 308,
"column": 2
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{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Monoid G\n⊢ QuasiIso (((forget₂ (Rep k G) (ModuleCat k)).mapHomologicalComplex (ComplexShape.down ℕ)).map (εToSingle₀ k G))",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Rep.V",
"CategoryTheory.Functor",
"ChainComplex... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 312,
"column": 40
} | {
"line": 312,
"column": 42
} | {
"line": 313,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn : ℕ\ninst✝ : Monoid G\n⊢ QuasiIso (εToSingle₀ k G)",
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"usedConstants": [
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"ChainComplex",
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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} | {
"line": 148,
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} | {
"line": 148,
"column": 49
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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Mathlib.RepresentationTheory.Homological.Resolution | {
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(X := Action.leftRegular G) (Y := Action.trivial G (Fin m → G)) g f 1 r | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RepresentationTheory.Homological.Resolution | {
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{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn : ℕ\ninst✝ : Group G\ni : Fin (n + 1) → G\neq3 :\n MonoidAlgebra.single (i 0 • Fin.partialProd fun i_1 ↦ i i_1.succ) 1 =\n MonoidAlgebra.single (Fin.partialProd i ∘ Fin.succ) 1\nm : ℕ\nf : Fin m → G\ng : G\nr : k\nstep1 :\n (Hom.hom (leftRegularTensorTrivialIso... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn : ℕ\ninst✝ : Group G\ni : Fin (n + 1) → G\neq3 :\n MonoidAlgebra.single (i 0 • Fin.partialProd fun i_1 ↦ i i_1.succ) 1 =\n MonoidAlgebra.single (Fin.partialProd i ∘ Fin.succ) 1\n⊢ ∀ (m : ℕ) (f : Fin m → G) (g : G) (r : k),\n (Hom.hom (diagonalSuccIsoFree k G ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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{
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Mathlib.RepresentationTheory.Homological.Resolution | {
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"ppTerm": "... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.Resolution | {
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Mathlib.RepresentationTheory.Homological.Resolution | {
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Mathlib.RepresentationTheory.Homological.Resolution | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\ny : (Fin i → G) → ↑X.X₂\nx : (Fin j → G) → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom ((inhomogeneousCochains X.X₂).d i j)) y\n⊢ (ConcreteCategory.hom (inhomogeneousCochains.d X.X... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
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{
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
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} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥X.X₃.ρ.invariants\ny : ↑X.X₂\nhy : (Rep.Hom.hom X.g) y = ↑z\nx : G → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom (d₀₁ X.X₂)) y\n⊢ (ConcreteCategory.hom (δ hX 0 1 ⋯)) ((ConcreteCategory... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 167,
"column": 26
} | {
"line": 167,
"column": 28
} | {
"line": 168,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ny : G → ↑X.X₂\nx : G × G → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom (d₁₂ X.X₂)) y\n⊢ x ∈ cocycles₂ X.X₁",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Pi.Fu... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 127,
"column": 36
} | {
"line": 127,
"column": 38
} | {
"line": 127,
"column": 39
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx y : G → ↑A\ng : G × G\n⊢ (A.ρ g.1) ((x + y) g.2) - (x + y) (g.1 * g.2) + (x + y) g.1 =\n ((fun g ↦ (A.ρ g.1) (x g.2) - x (g.1 * g.2) + x g.1) + fun g ↦ (A.ρ g.1) (y g.2) - y (g.1 * g.2) + y g.1) g",
"ppTerm": "?m.82",
"assign... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 128,
"column": 37
} | {
"line": 128,
"column": 39
} | {
"line": 128,
"column": 40
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nr : k\nx : G → ↑A\ng : G × G\n⊢ (A.ρ g.1) ((r • x) g.2) - (r • x) (g.1 * g.2) + (r • x) g.1 =\n ((RingHom.id k) r • fun g ↦ (A.ρ g.1) (x g.2) - x (g.1 * g.2) + x g.1) g",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants... | [] | by | [anonymous] | by |
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