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.Functoriality | {
"line": 117,
"column": 41
} | {
"line": 117,
"column": 43
} | {
"line": 118,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf g : G →* H\nφ : res f A ⟶ B\nψ : res g A ⟶ B\nhfg : f = g\nhφψ : (Hom.hom φ).toLinearMap = (Hom.hom ψ).toLinearMap\n⊢ cochainsMap f φ = cochainsMap g ψ",
"ppTerm": "?m.90",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 116,
"column": 76
} | {
"line": 116,
"column": 78
} | {
"line": 117,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝⁴ : CommRing k\ninst✝³ : CommGroup G\ninst✝² : Fintype G\nA : Rep k G\ng : G\ninst✝¹ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\ninst✝ : NeZero i\nhi : Even i\nx y : ↥(LinearMap.ker A.ρ.norm)\n⊢ (ConcreteCategory.hom (groupHomologyπEven A g hg i hi)) x =\n (C... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 126,
"column": 74
} | {
"line": 126,
"column": 76
} | {
"line": 126,
"column": 77
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\nA : Rep k G\ng : G\ninst✝ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nhi : Odd i\n⊢ ModuleCat.ofHom (Hom.hom A.norm).toLinearMap ≫ ModuleCat.ofHom (Hom.hom (A.applyAsHom g - 𝟙 A)).toLinearMap = 0",
"pp... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 129,
"column": 47
} | {
"line": 129,
"column": 49
} | {
"line": 130,
"column": 2
} | [
{
"pp": "k : Type u\ninst✝³ : CommRing k\nG H K : Type u\ninst✝² : Group G\ninst✝¹ : Group H\ninst✝ : Group K\nA : Rep k K\nB : Rep k H\nC : Rep k G\nf : H →* K\ng : G →* H\nφ : res f A ⟶ B\nψ : res g B ⟶ C\nn : ℕ\n⊢ cocyclesMap (f.comp g) ((resFunctor g).map φ ≫ ψ) n = cocyclesMap f φ n ≫ cocyclesMap g ψ n",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 127,
"column": 32
} | {
"line": 127,
"column": 34
} | {
"line": 127,
"column": 35
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\nA : Rep k G\ng : G\ninst✝ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nhi : Odd i\n⊢ ModuleCat.ofHom (Hom.hom (A.applyAsHom g - 𝟙 A)).toLinearMap ≫ ModuleCat.ofHom (Hom.hom A.norm).toLinearMap = 0",
"pp... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 135,
"column": 77
} | {
"line": 135,
"column": 79
} | {
"line": 136,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA B C : Rep k G\nφ : A ⟶ B\nψ : B ⟶ C\nn : ℕ\n⊢ cocyclesMap (MonoidHom.id G) (φ ≫ ψ) n = cocyclesMap (MonoidHom.id G) φ n ≫ cocyclesMap (MonoidHom.id G) ψ n",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"HomologicalComple... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 127,
"column": 83
} | {
"line": 127,
"column": 85
} | {
"line": 127,
"column": 86
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\nA : Rep k G\ng : G\ninst✝ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nhi : Odd i\n⊢ ∀ (i j : ℕ), (ComplexShape.down ℕ).Rel i j → Odd (i + j)",
"ppTerm": "?m.135",
"assigned": true,
"usedConstant... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 128,
"column": 5
} | {
"line": 128,
"column": 7
} | {
"line": 128,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\nA : Rep k G\ng : G\ninst✝ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nhi : Odd i\n⊢ (ComplexShape.down ℕ).Rel ((ComplexShape.down ℕ).prev i) i",
"ppTerm": "?m.136",
"assigned": true,
"usedConsta... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 128,
"column": 15
} | {
"line": 128,
"column": 17
} | {
"line": 128,
"column": 18
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\nA : Rep k G\ng : G\ninst✝ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nhi : Odd i\n⊢ (ComplexShape.down ℕ).Rel i ((ComplexShape.down ℕ).next i)",
"ppTerm": "?m.137",
"assigned": true,
"usedConsta... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 141,
"column": 76
} | {
"line": 141,
"column": 78
} | {
"line": 142,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\nA : Rep k G\ng : G\ninst✝ : DecidableEq G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ni : ℕ\nhi : Odd i\nx : ↥(Hom.hom (A.applyAsHom g - 𝟙 A)).ker\n⊢ (ConcreteCategory.hom (groupHomologyπOdd A g hg i hi)) x = 0 ↔ ↑x ∈ LinearMap.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 147,
"column": 29
} | {
"line": 147,
"column": 31
} | {
"line": 148,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf g : G →* H\nφ : res f A ⟶ B\nψ : res g A ⟶ B\nhfg : f = g\nhφψ : (Hom.hom φ).toLinearMap = (Hom.hom ψ).toLinearMap\nn : ℕ\n⊢ map f φ n = map g ψ n",
"ppTerm": "?m.90",
"assigned": true,
"used... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 153,
"column": 53
} | {
"line": 153,
"column": 55
} | {
"line": 154,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\n⊢ π A n ≫ map f φ n = cocyclesMap f φ n ≫ π B n",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"HomologicalComplex.homologyπ",
"groupC... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 164,
"column": 75
} | {
"line": 164,
"column": 77
} | {
"line": 165,
"column": 2
} | [
{
"pp": "k : Type u\ninst✝³ : CommRing k\nG H K : Type u\ninst✝² : Group G\ninst✝¹ : Group H\ninst✝ : Group K\nA : Rep k K\nB : Rep k H\nC : Rep k G\nf : H →* K\ng : G →* H\nφ : res f A ⟶ B\nψ : res g B ⟶ C\nn : ℕ\n⊢ map (f.comp g) ((resFunctor g).map φ ≫ ψ) n = map f φ n ≫ map g ψ n",
"ppTerm": "?m.94",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 148,
"column": 78
} | {
"line": 148,
"column": 80
} | {
"line": 149,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : CommGroup G\ninst✝¹ : Fintype G\ninst✝ : DecidableEq G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nA : Rep k G\ni : ℕ\nhi : Odd i\nx y : ↥(Hom.hom (A.applyAsHom g - 𝟙 A)).ker\n⊢ (ConcreteCategory.hom (groupHomologyπOdd A g hg i hi)) x = (ConcreteCategory... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 171,
"column": 61
} | {
"line": 171,
"column": 63
} | {
"line": 172,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA B C : Rep k G\nφ : A ⟶ B\nψ : B ⟶ C\nn : ℕ\n⊢ map (MonoidHom.id G) (φ ≫ ψ) n = map (MonoidHom.id G) φ n ≫ map (MonoidHom.id G) ψ n",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"groupCohomology.map.eq_1"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 180,
"column": 56
} | {
"line": 180,
"column": 58
} | {
"line": 180,
"column": 59
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\nh : H\n⊢ ↑e' ∘ₗ (MonoidHom.comp B.ρ ↑e.symm) h = A.ρ h ∘ₗ ↑e'",
"ppTerm": "?m.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 48,
"column": 13
} | {
"line": 48,
"column": 15
} | {
"line": 49,
"column": 6
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nthis : Mono X.f := hX.mono_f\ni : ℕ\n⊢ ((X.map (chainsFunctor k G)).map (HomologicalComplex.eval (ModuleCat k) (ComplexShape.down ℕ) i)).Exact",
"ppTerm": "?m.36",
"assigned": true,
"usedConst... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 117,
"column": 7
} | {
"line": 117,
"column": 9
} | {
"line": 117,
"column": 10
} | [
{
"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) →₀ ↑X.X₂\nx : (Fin j → G) →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom ((inhomogeneousChains X.X₂).d i j)) y\n⊢ (ConcreteCategory.ho... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 181,
"column": 56
} | {
"line": 181,
"column": 58
} | {
"line": 182,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\ng : G\n⊢ ↑e'.symm ∘ₗ (MonoidHom.comp A.ρ ↑e) g = B.ρ g ∘ₗ ↑e'.symm",
"ppTerm":... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 186,
"column": 21
} | {
"line": 186,
"column": 23
} | {
"line": 186,
"column": 24
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\n⊢ (↑e.symm).comp ↑e = MonoidHom.id G",
"ppTerm": "?m.303",
"assigned": tru... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 115,
"column": 24
} | {
"line": 115,
"column": 26
} | {
"line": 116,
"column": 4
} | [
{
"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) →₀ ↑X.X₂\nx : (Fin j → G) →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom ((inhomogeneousChains X.X₂).d i j)) y\n⊢ (ConcreteCategory.ho... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 186,
"column": 31
} | {
"line": 186,
"column": 33
} | {
"line": 186,
"column": 34
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\n⊢ (Hom.hom\n ((resFunctor ↑e).map (ofHom { toLinearMap := ↑e', isIntertwini... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 184,
"column": 16
} | {
"line": 184,
"column": 18
} | {
"line": 185,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\n⊢ map (↑e.symm) (ofHom { toLinearMap := ↑e', isIntertwining' := ⋯ }) n ≫\n ma... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 189,
"column": 37
} | {
"line": 189,
"column": 39
} | {
"line": 189,
"column": 40
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\n⊢ (↑e).comp ↑e.symm = MonoidHom.id H",
"ppTerm": "?m.342",
"assigned": tru... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 130,
"column": 44
} | {
"line": 130,
"column": 46
} | {
"line": 130,
"column": 47
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : j + 1 = i\nz : (Fin i → G) →₀ ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousChains X.X₃).d i j)) z = 0\ny : (Fin i → G) →₀ ↑X.X₂\nhy : (ConcreteCategory.hom ((chainsMap (MonoidHom.id G) ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 187,
"column": 16
} | {
"line": 187,
"column": 18
} | {
"line": 188,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ : ℕ\ne : G ≃* H\ne' : ↑B ≃ₗ[k] ↑A\nhe : ∀ (g : G), ↑e' ∘ₗ B.ρ g = A.ρ (e g) ∘ₗ ↑e'\nn : ℕ\n⊢ map (↑e) (ofHom { toLinearMap := ↑e'.symm, isIntertwining' := ⋯ }) n ≫\n ma... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 130,
"column": 64
} | {
"line": 130,
"column": 66
} | {
"line": 130,
"column": 67
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : j + 1 = i\nz : (Fin i → G) →₀ ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousChains X.X₃).d i j)) z = 0\ny : (Fin i → G) →₀ ↑X.X₂\nhy : (ConcreteCategory.hom ((chainsMap (MonoidHom.id G) ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 213,
"column": 94
} | {
"line": 213,
"column": 96
} | {
"line": 214,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ (cochainsMap f φ).f 0 ≫ (cochainsIso₀ B).hom = (cochainsIso₀ A).hom ≫ Hom.toModuleCatHom φ",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 132,
"column": 71
} | {
"line": 132,
"column": 73
} | {
"line": 132,
"column": 74
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : j + 1 = i\nz : (Fin i → G) →₀ ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousChains X.X₃).d i j)) z = 0\ny : (Fin i → G) →₀ ↑X.X₂\nhy : (ConcreteCategory.hom ((chainsMap (MonoidHom.id G) ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 131,
"column": 44
} | {
"line": 131,
"column": 46
} | {
"line": 132,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : j + 1 = i\nz : (Fin i → G) →₀ ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousChains X.X₃).d i j)) z = 0\ny : (Fin i → G) →₀ ↑X.X₂\nhy : (ConcreteCategory.hom ((chainsMap (MonoidHom.id G) ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 145,
"column": 71
} | {
"line": 145,
"column": 73
} | {
"line": 146,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₁ X.X₃)\ny : G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : ↑X.X₁\nhx : (Rep.Hom.hom X.f) x = (ConcreteCategory.hom (d₁₀ X.X₂)) y\n⊢ (ConcreteCategory.hom ((in... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 147,
"column": 52
} | {
"line": 147,
"column": 54
} | {
"line": 147,
"column": 55
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₁ X.X₃)\ny : G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : ↑X.X₁\nhx : (Rep.Hom.hom X.f) x = (ConcreteCategory.hom (d₁₀ X.X₂)) y\nx✝ : Fin 1 → G\n⊢ ((Concrete... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 224,
"column": 94
} | {
"line": 224,
"column": 96
} | {
"line": 225,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ (cochainsMap f φ).f 2 ≫ (cochainsIso₂ B).hom = (cochainsIso₂ A).hom ≫ cochainsMap₂ f φ",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Pi.Functio... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 148,
"column": 52
} | {
"line": 148,
"column": 54
} | {
"line": 149,
"column": 6
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₁ X.X₃)\ny : G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : ↑X.X₁\nhx : (Rep.Hom.hom X.f) x = (ConcreteCategory.hom (d₁₀ X.X₂)) y\nx✝ : Fin 0 → G\n⊢ ((mapRange... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 142,
"column": 46
} | {
"line": 142,
"column": 48
} | {
"line": 143,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₁ X.X₃)\ny : G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : ↑X.X₁\nhx : (Rep.Hom.hom X.f) x = (ConcreteCategory.hom (d₁₀ X.X₂)) y\n⊢ (ConcreteCategory.hom (δ h... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 157,
"column": 86
} | {
"line": 157,
"column": 88
} | {
"line": 158,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ny : G × G →₀ ↑X.X₂\nx : G →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom (d₂₁ X.X₂)) y\n⊢ (Rep.Hom.hom X.f) ((ModuleCat.Hom.hom (d₁₀ X.X₁)) x) = (Rep.Hom.hom X... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 232,
"column": 94
} | {
"line": 232,
"column": 96
} | {
"line": 233,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ (cochainsMap f φ).f 3 ≫ (cochainsIso₃ B).hom = (cochainsIso₃ A).hom ≫ cochainsMap₃ f φ",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Pi.Functio... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 248,
"column": 65
} | {
"line": 248,
"column": 67
} | {
"line": 249,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ map f φ 0 ≫ (H0Iso B).hom ≫ (shortComplexH0 B).f = (H0Iso A).hom ≫ (shortComplexH0 A).f ≫ Hom.toModuleCatHom φ",
"ppTerm": "?m.82",
"assigned": true,
"usedConstan... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 254,
"column": 96
} | {
"line": 254,
"column": 98
} | {
"line": 255,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA B : Rep k G\nf : A ⟶ B\n⊢ map (MonoidHom.id G) f 0 ≫ (H0Iso B).hom = (H0Iso A).hom ≫ (invariantsFunctor k G).map f",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Rep.invariantsFunctor",
"CategoryTh... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 261,
"column": 32
} | {
"line": 261,
"column": 34
} | {
"line": 262,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA✝ : Rep k H\nB✝ : Rep k G\nf✝ : G →* H\nφ : res f✝ A✝ ⟶ B✝\nn : ℕ\nA B : Rep k G\nf : A ⟶ B\ninst✝ : Mono f\nZ✝ : ModuleCat k\ng h : Z✝ ⟶ groupCohomology A 0\nhgh : g ≫ map (MonoidHom.id G) f 0 = h ≫ map (MonoidHom.id G) f 0\n⊢ g... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 269,
"column": 72
} | {
"line": 269,
"column": 74
} | {
"line": 270,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ cocyclesMap f φ 0 ≫ (cocyclesIso₀ B).hom ≫ (shortComplexH0 B).f =\n (cocyclesIso₀ A).hom ≫ (shortComplexH0 A).f ≫ Hom.toModuleCatHom φ",
"ppTerm": "?m.82",
"assign... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 172,
"column": 71
} | {
"line": 172,
"column": 73
} | {
"line": 173,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₂ X.X₃)\ny : G × G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : G →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 285,
"column": 12
} | {
"line": 285,
"column": 14
} | {
"line": 286,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\n⊢ Hom.toModuleCatHom φ ≫ (shortComplexH1 B).f = (shortComplexH1 A).f ≫ cochainsMap₁ f φ",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.m... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 174,
"column": 52
} | {
"line": 174,
"column": 54
} | {
"line": 174,
"column": 55
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₂ X.X₃)\ny : G × G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : G →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 289,
"column": 12
} | {
"line": 289,
"column": 14
} | {
"line": 290,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\n⊢ cochainsMap₁ f φ ≫ (shortComplexH1 B).g = (shortComplexH1 A).g ≫ cochainsMap₂ f φ",
"ppTerm": "?m.101",
"assigned": true,
"usedConstants": [
"Eq.mpr"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 296,
"column": 51
} | {
"line": 296,
"column": 53
} | {
"line": 297,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\n⊢ mapShortComplexH1 f 0 = 0",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"C... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 301,
"column": 54
} | {
"line": 301,
"column": 56
} | {
"line": 302,
"column": 2
} | [
{
"pp": "k H : Type u\ninst✝¹ : CommRing k\ninst✝ : Group H\nA : Rep k H\n⊢ mapShortComplexH1 (MonoidHom.id H) (𝟙 A) = 𝟙 (shortComplexH1 A)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"Monoid... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 327,
"column": 75
} | {
"line": 327,
"column": 77
} | {
"line": 328,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ mapCocycles₁ f φ ≫ (shortComplexH1 B).moduleCatLeftHomologyData.i =\n (shortComplexH1 A).moduleCatLeftHomologyData.i ≫ cochainsMap₁ f φ",
"ppTerm": "?m.62",
"assig... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 337,
"column": 97
} | {
"line": 337,
"column": 99
} | {
"line": 338,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ cocyclesMap f φ 1 ≫ (isoCocycles₁ B).hom = (isoCocycles₁ A).hom ≫ mapCocycles₁ f φ",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"groupCohomolog... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 344,
"column": 28
} | {
"line": 344,
"column": 30
} | {
"line": 345,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nφ : res 1 A ⟶ B\n⊢ mapCocycles₁ 1 φ = 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
"Submodule",
"Rep.V",
"groupCohom... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 352,
"column": 52
} | {
"line": 352,
"column": 54
} | {
"line": 353,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ H1π A ≫ map f φ 1 = mapCocycles₁ f φ ≫ H1π B",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"CategoryTheory.Category.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 357,
"column": 21
} | {
"line": 357,
"column": 23
} | {
"line": 358,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nφ : res 1 A ⟶ B\n⊢ map 1 φ 1 = 0",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"Submodule",
"Rep.V",
"CommRing",
"groupCohomology... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 175,
"column": 52
} | {
"line": 175,
"column": 54
} | {
"line": 176,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₂ X.X₃)\ny : G × G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : G →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 373,
"column": 10
} | {
"line": 373,
"column": 12
} | {
"line": 373,
"column": 13
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA✝ : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A✝ ⟶ B\nn : ℕ\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\n⊢ map (QuotientGroup.mk' S) (ofHom (A.ρ.quotientToInvariants_lift S)) 1 ≫ map S.subtype (𝟙 (res S.subtype A)) 1 = 0",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 169,
"column": 82
} | {
"line": 169,
"column": 84
} | {
"line": 170,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₂ X.X₃)\ny : G × G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : G →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 67,
"column": 91
} | {
"line": 67,
"column": 93
} | {
"line": 68,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\n⊢ M.tateNorm = ModuleCat.ofHom ((Finsupp.lsum R) fun x ↦ LinearMap.pi fun x ↦ M.ρ.norm)",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Pi.Function.module",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 72,
"column": 69
} | {
"line": 72,
"column": 71
} | {
"line": 73,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\n⊢ Hom.toModuleCatHom M.norm ≫ d₀₁ M = 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"Rep.V",
"Representation",
"MonoidHom.instFunLike",
"Lin... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 76,
"column": 80
} | {
"line": 76,
"column": 82
} | {
"line": 77,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\n⊢ M.tateNorm ≫ (inhomogeneousCochains M).d 0 1 = 0",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"inhomogeneousCochains.d",
"CategoryTheory.Category.assoc... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 80,
"column": 62
} | {
"line": 80,
"column": 64
} | {
"line": 81,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\n⊢ d₁₀ M ≫ Hom.toModuleCatHom M.norm = 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Rep.V",
"Representation",
"MonoidHom.instFunLike",
"LinearMap.comp.congr_simp",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 84,
"column": 78
} | {
"line": 84,
"column": 80
} | {
"line": 85,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\n⊢ (inhomogeneousChains M).d 1 0 ≫ M.tateNorm = 0",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
"CategoryTheory.Category.assoc",
"Rep.V",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 386,
"column": 28
} | {
"line": 386,
"column": 30
} | {
"line": 386,
"column": 31
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA✝ : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A✝ ⟶ B\nn : ℕ\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cocycles₁ (A.quotientToInvariants S))\nhx :\n (ConcreteCategory.hom (H1π (of A.ρ)))\n ((ConcreteCategory.ho... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 110,
"column": 67
} | {
"line": 110,
"column": 69
} | {
"line": 111,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\nX Y : Rep R G\nφ : X ⟶ Y\n⊢ tateComplex X ⟶ tateComplex Y",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"tateComplexConnectData_d₀",
"Pi.Function.module",
"CategoryTheory.Categ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 116,
"column": 64
} | {
"line": 116,
"column": 66
} | {
"line": 116,
"column": 67
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nX Y : Rep R G\n⊢ map 0 = 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HomologicalComplex.hom_ext",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 379,
"column": 36
} | {
"line": 379,
"column": 38
} | {
"line": 380,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA✝ : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A✝ ⟶ B\nn : ℕ\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\n⊢ Mono (H1InfRes A S).f",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Rep.quotientToInva... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 120,
"column": 45
} | {
"line": 120,
"column": 47
} | {
"line": 121,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nX Y : Rep R G\nf g : X ⟶ Y\n⊢ map (f + g) = map f + map g",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"HomologicalComplex.hom_ext",
"Rep.V",
"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 135,
"column": 18
} | {
"line": 135,
"column": 20
} | {
"line": 136,
"column": 4
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\nX : Rep R G\nY : Rep R G\nX✝ Y✝ Z✝ : Rep R G\nf : X✝ ⟶ Y✝\ng : Y✝ ⟶ Z✝\n⊢ tateComplex.map (f ≫ g) = tateComplex.map f ≫ tateComplex.map g",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Rep... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 153,
"column": 18
} | {
"line": 153,
"column": 20
} | {
"line": 153,
"column": 21
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nM : Rep R G\nX✝ : Rep R G\nY✝ : Rep R G\nX Y : Rep R G\n⊢ (tateComplexFunctor R G).map 0 = 0",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"HomologicalComplex.instCategory",
"CategoryTheory.Categ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 172,
"column": 51
} | {
"line": 172,
"column": 53
} | {
"line": 173,
"column": 2
} | [
{
"pp": "R G : Type u\ninst✝² : CommRing R\ninst✝¹ : Group G\ninst✝ : Fintype G\nS : ShortComplex (Rep R G)\nhS : S.ShortExact\n⊢ (S.map (tateComplexFunctor R G)).ShortExact",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"CategoryTheory.Abelian.toPreadd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 234,
"column": 96
} | {
"line": 234,
"column": 98
} | {
"line": 235,
"column": 4
} | [
{
"pp": "R G : Type u\ninst✝³ : CommRing R\ninst✝² : Group G\ninst✝¹ : Fintype G\nM : Rep R G\nX✝ : Rep R G\nY✝ : Rep R G\nn : ℕ\ninst✝ : NeZero n\nX Y : Rep R G\nf : X ⟶ Y\n⊢ (tateCohomologyFunctor ↑n).map f ≫ ((tateComplexConnectData Y).homologyIsoPos n ↑n ⋯).hom =\n ((tateComplexConnectData X).homologyIso... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.TateCohomology.Basic | {
"line": 242,
"column": 96
} | {
"line": 242,
"column": 98
} | {
"line": 243,
"column": 4
} | [
{
"pp": "R G : Type u\ninst✝³ : CommRing R\ninst✝² : Group G\ninst✝¹ : Fintype G\nM : Rep R G\nX✝ : Rep R G\nY✝ : Rep R G\nm : ℤ\nn : ℕ\nhmn : m = -(↑n + 1)\ninst✝ : NeZero n\nX Y : Rep R G\nf : X ⟶ Y\n⊢ (tateCohomologyFunctor m).map f ≫ ((tateComplexConnectData Y).homologyIsoNeg n m hmn).hom =\n ((tateCompl... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 407,
"column": 59
} | {
"line": 407,
"column": 61
} | {
"line": 408,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cocycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (res S.subtype A)))\n ((ConcreteCategory.hom (mapCocycles₁ S.subtype (𝟙 (res S.subtype A)))) x) =\n 0\ny : ↑A\nhy :\n (ModuleCat.Hom.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 409,
"column": 83
} | {
"line": 409,
"column": 85
} | {
"line": 410,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cocycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (res S.subtype A)))\n ((ConcreteCategory.hom (mapCocycles₁ S.subtype (𝟙 (res S.subtype A)))) x) =\n 0\ny : ↑A\nhy :\n (ModuleCat.Hom.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 413,
"column": 31
} | {
"line": 413,
"column": 33
} | {
"line": 414,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cocycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (res S.subtype A)))\n ((ConcreteCategory.hom (mapCocycles₁ S.subtype (𝟙 (res S.subtype A)))) x) =\n 0\ny : ↑A\nhy :\n (ModuleCat.Hom.hom (... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 59,
"column": 16
} | {
"line": 59,
"column": 18
} | {
"line": 60,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\ng : G\nX : FDRep k G\n⊢ InducedCategory.homMk (↟(X.ρ g)) ≫ InducedCategory.homMk (↟(X.ρ g⁻¹)) = 𝟙 X.V",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"CategoryTheory.InducedCategory.homMk_hom",
"MonoidHom.instFunLike... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 62,
"column": 16
} | {
"line": 62,
"column": 18
} | {
"line": 63,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\ng : G\nX : FDRep k G\n⊢ InducedCategory.homMk (↟(X.ρ g⁻¹)) ≫ InducedCategory.homMk (↟(X.ρ g)) = 𝟙 X.V",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"CategoryTheory.InducedCategory.homMk_hom",
"MonoidHom.instFunLike... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 72,
"column": 83
} | {
"line": 72,
"column": 85
} | {
"line": 72,
"column": 86
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\ng : G\n⊢ ∀ (X Y : FDRep k G),\n Functor.LaxMonoidal.μ (forget k G).toFunctor X Y ≫ (equivApp g (X ⊗ Y)).hom =\n ((equivApp g X).hom ⊗ₘ (equivApp g Y).hom) ≫ Functor.LaxMonoidal.μ (forget k G).toFunctor X Y",
"ppTerm": "?m.43",
"assigne... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 73,
"column": 14
} | {
"line": 73,
"column": 16
} | {
"line": 73,
"column": 17
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\n⊢ LaxMonoidalFunctor.isoOfComponents (equivApp 1) ⋯ ⋯ ⋯ = 1",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"CategoryTheory.InducedCategory.homMk_hom",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MulOne.toO... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 74,
"column": 18
} | {
"line": 74,
"column": 20
} | {
"line": 74,
"column": 21
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nx✝¹ x✝ : G\n⊢ LaxMonoidalFunctor.isoOfComponents (equivApp (x✝¹ * x✝)) ⋯ ⋯ ⋯ =\n LaxMonoidalFunctor.isoOfComponents (equivApp x✝¹) ⋯ ⋯ ⋯ * LaxMonoidalFunctor.isoOfComponents (equivApp x✝) ⋯ ⋯ ⋯",
"ppTerm": "?m.104",
"assigned": true,
"u... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 82,
"column": 14
} | {
"line": 82,
"column": 16
} | {
"line": 83,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\n⊢ { toFun := fun f t ↦ f (t * 1), map_add' := ⋯, map_smul' := ⋯ } = 1",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"AddHom.mk.congr_simp",
"Pi.Function.module",
"MulOne.toOne",
"instHSMul",
"Semir... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 85,
"column": 18
} | {
"line": 85,
"column": 20
} | {
"line": 86,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nx✝¹ x✝ : G\n⊢ { toFun := fun f t ↦ f (t * (x✝¹ * x✝)), map_add' := ⋯, map_smul' := ⋯ } =\n { toFun := fun f t ↦ f (t * x✝¹), map_add' := ⋯, map_smul' := ⋯ } *\n { toFun := fun f t ↦ f (t * x✝), map_add' := ⋯, map_smul' := ⋯ }",
"ppTerm": "... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 98,
"column": 14
} | {
"line": 98,
"column": 16
} | {
"line": 99,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\n⊢ { toFun := fun f t ↦ f (1⁻¹ * t), map_add' := ⋯, map_smul' := ⋯ } = 1",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"AddHom.mk.congr_simp",
"Pi.Function.module",
"MulOne.toOne",
"instHSMul",
"Sem... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 101,
"column": 18
} | {
"line": 101,
"column": 20
} | {
"line": 102,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nx✝¹ x✝ : G\n⊢ { toFun := fun f t ↦ f ((x✝¹ * x✝)⁻¹ * t), map_add' := ⋯, map_smul' := ⋯ } =\n { toFun := fun f t ↦ f (x✝¹⁻¹ * t), map_add' := ⋯, map_smul' := ⋯ } *\n { toFun := fun f t ↦ f (x✝⁻¹ * t), map_add' := ⋯, map_smul' := ⋯ }",
"ppTe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 117,
"column": 79
} | {
"line": 117,
"column": 81
} | {
"line": 118,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Finite G\ninst✝ : Nontrivial k\n⊢ Function.Injective ⇑(equivHom k G)",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"CategoryTheory.InducedCategory.homMk_hom",
"Pi.Function.module",
"CategoryTheory.Fun... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 126,
"column": 10
} | {
"line": 126,
"column": 12
} | {
"line": 127,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Finite G\n⊢ ∀ (g : G),\n (rightFDRep ⊗ rightFDRep).ρ g ≫ InducedCategory.homMk (↟(LinearMap.mul' k (G → k))) =\n InducedCategory.homMk (↟(LinearMap.mul' k (G → k))) ≫ rightFDRep.ρ g",
"ppTerm": "?m.45",
"assigned": true,
"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 135,
"column": 33
} | {
"line": 135,
"column": 35
} | {
"line": 136,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Finite G\nη : Aut (forget k G)\nf g : G → k\n⊢ let α := Hom.hom (η.hom.hom.app rightFDRep).hom;\n α (f * g) = α f * α g",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"Semiring.toModul... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 149,
"column": 37
} | {
"line": 149,
"column": 39
} | {
"line": 150,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Finite G\nη : Aut (forget k G)\nα : (G → k) →ₗ[k] G → k := Hom.hom (η.hom.hom.app rightFDRep).hom\nα_inv : (G → k) →ₗ[k] G → k := Hom.hom (η.inv.hom.app rightFDRep).hom\nthis : α (α_inv 1) = 1\n⊢ α 1 = 1",
"ppTerm": "?m.123",
"assigne... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 394,
"column": 47
} | {
"line": 394,
"column": 49
} | {
"line": 395,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\n⊢ (H1InfRes A S).Exact",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Rep.quotientToInvariants",
"groupCohomology.H1InfRes",
"Eq.mpr",
"Pi.Function.module"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 145,
"column": 77
} | {
"line": 145,
"column": 79
} | {
"line": 146,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Finite G\nη : Aut (forget k G)\n⊢ (G → k) →ₐ[k] G → k",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"CategoryTheory.Functor",
"Semiring.toModule",
"Pi.addCommMonoid",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 161,
"column": 18
} | {
"line": 161,
"column": 20
} | {
"line": 161,
"column": 21
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Finite G\ninst✝ : Fintype G\nX : FDRep k G\nv : ↑X.V\nx✝¹ x✝ : G → k\n⊢ ∑ s, (x✝¹ + x✝) s • (X.ρ s⁻¹) v = ∑ s, x✝¹ s • (X.ρ s⁻¹) v + ∑ s, x✝ s • (X.ρ s⁻¹) v",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"instHSM... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 162,
"column": 19
} | {
"line": 162,
"column": 21
} | {
"line": 162,
"column": 22
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Finite G\ninst✝ : Fintype G\nX : FDRep k G\nv : ↑X.V\nx✝¹ : k\nx✝ : G → k\n⊢ ∑ s, (x✝¹ • x✝) s • (X.ρ s⁻¹) v = (RingHom.id k) x✝¹ • ∑ s, x✝ s • (X.ρ s⁻¹) v",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Pi.Funct... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 166,
"column": 57
} | {
"line": 166,
"column": 59
} | {
"line": 167,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Fintype G\ninst✝ : DecidableEq G\nX : FDRep k G\nv : ↑X.V\n⊢ ∑ s, single 1 1 s • (X.ρ s⁻¹) v = v",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"MonoidHom.instMonoidHomClass",
"instHSMul",
"MonoidHom.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 447,
"column": 12
} | {
"line": 447,
"column": 14
} | {
"line": 448,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\n⊢ cochainsMap₁ f φ ≫ (shortComplexH2 B).f = (shortComplexH2 A).f ≫ cochainsMap₂ f φ",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Pi.Funct... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Tannaka | {
"line": 175,
"column": 12
} | {
"line": 175,
"column": 14
} | {
"line": 176,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Finite G\ninst✝ : Fintype G\nX : FDRep k G\nv : ↑X.V\nt : G\n⊢ rightFDRep.ρ t ≫ InducedCategory.homMk (↟(sumSMulInv v)) = InducedCategory.homMk (↟(sumSMulInv v)) ≫ X.ρ t",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 451,
"column": 12
} | {
"line": 451,
"column": 14
} | {
"line": 452,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\n⊢ cochainsMap₂ f φ ≫ (shortComplexH2 B).g = (shortComplexH2 A).g ≫ cochainsMap₃ f φ",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"groupCoh... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 462,
"column": 54
} | {
"line": 462,
"column": 56
} | {
"line": 463,
"column": 2
} | [
{
"pp": "k H : Type u\ninst✝¹ : CommRing k\ninst✝ : Group H\nA : Rep k H\n⊢ mapShortComplexH2 (MonoidHom.id H) (𝟙 A) = 𝟙 (shortComplexH2 A)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"Monoid... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 488,
"column": 75
} | {
"line": 488,
"column": 77
} | {
"line": 489,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ mapCocycles₂ f φ ≫ (shortComplexH2 B).moduleCatLeftHomologyData.i =\n (shortComplexH2 A).moduleCatLeftHomologyData.i ≫ cochainsMap₂ f φ",
"ppTerm": "?m.62",
"assig... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 498,
"column": 90
} | {
"line": 498,
"column": 92
} | {
"line": 499,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ cocyclesMap f φ 2 ≫ (isoCocycles₂ B).hom = (isoCocycles₂ A).hom ≫ mapCocycles₂ f φ",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"Pi.Function.mo... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 505,
"column": 52
} | {
"line": 505,
"column": 54
} | {
"line": 506,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\n⊢ H2π A ≫ map f φ 2 = mapCocycles₂ f φ ≫ H2π B",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"CategoryTheory.Category.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 530,
"column": 18
} | {
"line": 530,
"column": 20
} | {
"line": 531,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ n : ℕ\nX✝ Y✝ Z✝ : Rep k G\nx✝¹ : X✝ ⟶ Y✝\nx✝ : Y✝ ⟶ Z✝\n⊢ map (MonoidHom.id G) (x✝¹ ≫ x✝) n = map (MonoidHom.id G) x✝¹ n ≫ map (MonoidHom.id G) x✝ n",
"ppTerm": "?m.54",... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 536,
"column": 18
} | {
"line": 536,
"column": 20
} | {
"line": 536,
"column": 21
} | [
{
"pp": "k G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn✝ n : ℕ\nx✝¹ x✝ : Rep k G\n⊢ (functor k G n).map 0 = 0",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"HomologicalComplex.instCategory",
"gr... | [] | by | [anonymous] | by |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.