Loogle!

Result

Found 45 declarations mentioning groupCohomology.map.

• groupCohomology.H0Map_id 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {B : Rep k G} (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.id B) n = CategoryTheory.CategoryStruct.id (groupCohomology B n)
• groupCohomology.H1Map_id 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {B : Rep k G} (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.id B) n = CategoryTheory.CategoryStruct.id (groupCohomology B n)
• groupCohomology.H2Map_id 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {B : Rep k G} (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.id B) n = CategoryTheory.CategoryStruct.id (groupCohomology B n)
• groupCohomology.map_id 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {B : Rep k G} (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.id B) n = CategoryTheory.CategoryStruct.id (groupCohomology B n)
• groupCohomology.mono_H0Map_of_mono 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B : Rep k G} (f : A ⟶ B) [CategoryTheory.Mono f] : CategoryTheory.Mono (groupCohomology.map (MonoidHom.id G) f 0)
• groupCohomology.mono_map_0_of_mono 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B : Rep k G} (f : A ⟶ B) [CategoryTheory.Mono f] : CategoryTheory.Mono (groupCohomology.map (MonoidHom.id G) f 0)
• groupCohomology.functor_map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  (k G : Type u) [CommRing k] [Group G] (n : ℕ) {X✝ Y✝ : Rep k G} (φ : X✝ ⟶ Y✝) : (groupCohomology.functor k G n).map φ = groupCohomology.map (MonoidHom.id G) φ n
• groupCohomology.map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (n : ℕ) : groupCohomology A n ⟶ groupCohomology B n
• groupCohomology.map.eq_1 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (n : ℕ) : groupCohomology.map f φ n = HomologicalComplex.homologyMap (groupCohomology.cochainsMap f φ) n
• groupCohomology.π_map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (n : ℕ) : CategoryTheory.CategoryStruct.comp (groupCohomology.π A n) (groupCohomology.map f φ n) = CategoryTheory.CategoryStruct.comp (groupCohomology.cocyclesMap f φ n) (groupCohomology.π B n)
• groupCohomology.H0Map_id_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B C : Rep k G} (φ : A ⟶ B) (ψ : B ⟶ C) (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.comp φ ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) φ n) (groupCohomology.map (MonoidHom.id G) ψ n)
• groupCohomology.H1Map_id_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B C : Rep k G} (φ : A ⟶ B) (ψ : B ⟶ C) (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.comp φ ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) φ n) (groupCohomology.map (MonoidHom.id G) ψ n)
• groupCohomology.H2Map_id_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B C : Rep k G} (φ : A ⟶ B) (ψ : B ⟶ C) (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.comp φ ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) φ n) (groupCohomology.map (MonoidHom.id G) ψ n)
• groupCohomology.map_id_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B C : Rep k G} (φ : A ⟶ B) (ψ : B ⟶ C) (n : ℕ) : groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.comp φ ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) φ n) (groupCohomology.map (MonoidHom.id G) ψ n)
• groupCohomology.π_map_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (n : ℕ) {Z : ModuleCat k} (h : groupCohomology B n ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.π A n) (CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ n) h) = CategoryTheory.CategoryStruct.comp (groupCohomology.cocyclesMap f φ n) (CategoryTheory.CategoryStruct.comp (groupCohomology.π B n) h)
• groupCohomology.H1Map_one 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (φ : (Action.res (ModuleCat k) 1).obj A ⟶ B) : groupCohomology.map 1 φ 1 = 0
• groupCohomology.map_1_one 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (φ : (Action.res (ModuleCat k) 1).obj A ⟶ B) : groupCohomology.map 1 φ 1 = 0
• groupCohomology.map₁_one 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (φ : (Action.res (ModuleCat k) 1).obj A ⟶ B) : groupCohomology.map 1 φ 1 = 0
• groupCohomology.map_id_comp_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B C : Rep k G} (φ : A ⟶ B) (ψ : B ⟶ C) (n : ℕ) {Z : ModuleCat k} (h : groupCohomology C n ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) (CategoryTheory.CategoryStruct.comp φ ψ) n) h = CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) φ n) (CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) ψ n) h)
• groupCohomology.resNatTrans_app 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  (k : Type u) {G H : Type u} [CommRing k] [Group G] [Group H] (f : G →* H) (n : ℕ) (X : Rep k H) : (groupCohomology.resNatTrans k f n).app X = groupCohomology.map f (CategoryTheory.CategoryStruct.id ((Action.res (ModuleCat k) f).obj X)) n
• groupCohomology.H1InfRes_f 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] (A : Rep k G) (S : Subgroup G) [S.Normal] : (groupCohomology.H1InfRes A S).f = groupCohomology.map (QuotientGroup.mk' S) (A.subtype (Representation.invariants (MonoidHom.comp A.ρ S.subtype)) ⋯) 1
• groupCohomology.H0Map_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k : Type u} [CommRing k] {G H K : Type u} [Group G] [Group H] [Group K] {A : Rep k K} {B : Rep k H} {C : Rep k G} (f : H →* K) (g : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (ψ : (Action.res (ModuleCat k) g).obj B ⟶ C) (n : ℕ) : groupCohomology.map (f.comp g) (CategoryTheory.CategoryStruct.comp ((Action.res (ModuleCat k) g).map φ) ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ n) (groupCohomology.map g ψ n)
• groupCohomology.H1Map_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k : Type u} [CommRing k] {G H K : Type u} [Group G] [Group H] [Group K] {A : Rep k K} {B : Rep k H} {C : Rep k G} (f : H →* K) (g : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (ψ : (Action.res (ModuleCat k) g).obj B ⟶ C) (n : ℕ) : groupCohomology.map (f.comp g) (CategoryTheory.CategoryStruct.comp ((Action.res (ModuleCat k) g).map φ) ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ n) (groupCohomology.map g ψ n)
• groupCohomology.H2Map_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k : Type u} [CommRing k] {G H K : Type u} [Group G] [Group H] [Group K] {A : Rep k K} {B : Rep k H} {C : Rep k G} (f : H →* K) (g : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (ψ : (Action.res (ModuleCat k) g).obj B ⟶ C) (n : ℕ) : groupCohomology.map (f.comp g) (CategoryTheory.CategoryStruct.comp ((Action.res (ModuleCat k) g).map φ) ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ n) (groupCohomology.map g ψ n)
• groupCohomology.map_comp 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k : Type u} [CommRing k] {G H K : Type u} [Group G] [Group H] [Group K] {A : Rep k K} {B : Rep k H} {C : Rep k G} (f : H →* K) (g : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (ψ : (Action.res (ModuleCat k) g).obj B ⟶ C) (n : ℕ) : groupCohomology.map (f.comp g) (CategoryTheory.CategoryStruct.comp ((Action.res (ModuleCat k) g).map φ) ψ) n = CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ n) (groupCohomology.map g ψ n)
• groupCohomology.infNatTrans_app 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  (k : Type u) {G : Type u} [CommRing k] [Group G] (S : Subgroup G) [S.Normal] (n : ℕ) (A : Rep k G) : (groupCohomology.infNatTrans k S n).app A = groupCohomology.map (QuotientGroup.mk' S) (A.subtype (Representation.invariants (MonoidHom.comp A.ρ S.subtype)) ⋯) n
• groupCohomology.map_comp_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k : Type u} [CommRing k] {G H K : Type u} [Group G] [Group H] [Group K] {A : Rep k K} {B : Rep k H} {C : Rep k G} (f : H →* K) (g : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (ψ : (Action.res (ModuleCat k) g).obj B ⟶ C) (n : ℕ) {Z : ModuleCat k} (h : groupCohomology C n ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map (f.comp g) (CategoryTheory.CategoryStruct.comp ((Action.res (ModuleCat k) g).map φ) ψ) n) h = CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ n) (CategoryTheory.CategoryStruct.comp (groupCohomology.map g ψ n) h)
• groupCohomology.H1InfRes_g 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] (A : Rep k G) (S : Subgroup G) [S.Normal] : (groupCohomology.H1InfRes A S).g = groupCohomology.map S.subtype (CategoryTheory.CategoryStruct.id ((Action.res (ModuleCat k) S.subtype).obj A)) 1
• groupCohomology.π_map_apply 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (n : ℕ) (x : CategoryTheory.ToType (groupCohomology.cocycles A n)) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ n)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.π A n)) x) = (CategoryTheory.ConcreteCategory.hom (groupCohomology.π B n)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.cocyclesMap f φ n)) x)
• groupCohomology.H0Map_id_eq_invariantsFunctor_map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B : Rep k G} (f : A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) f 0) (groupCohomology.H0Iso B).hom = CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom ((Rep.invariantsFunctor k G).map f)
• groupCohomology.map_id_comp_H0Iso_hom 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B : Rep k G} (f : A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) f 0) (groupCohomology.H0Iso B).hom = CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom ((Rep.invariantsFunctor k G).map f)
• groupCohomology.H1π_comp_H1Map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.H1π A) (groupCohomology.map f φ 1) = CategoryTheory.CategoryStruct.comp (groupCohomology.mapCocycles₁ f φ) (groupCohomology.H1π B)
• groupCohomology.H1π_comp_map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.H1π A) (groupCohomology.map f φ 1) = CategoryTheory.CategoryStruct.comp (groupCohomology.mapCocycles₁ f φ) (groupCohomology.H1π B)
• groupCohomology.H2π_comp_H2Map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.H2π A) (groupCohomology.map f φ 2) = CategoryTheory.CategoryStruct.comp (groupCohomology.mapCocycles₂ f φ) (groupCohomology.H2π B)
• groupCohomology.H2π_comp_map 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.H2π A) (groupCohomology.map f φ 2) = CategoryTheory.CategoryStruct.comp (groupCohomology.mapCocycles₂ f φ) (groupCohomology.H2π B)
• groupCohomology.H0Map_comp_f 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 0) (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso B).hom (groupCohomology.shortComplexH0 B).f) = CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 A).f φ.hom)
• groupCohomology.map_H0Iso_hom_f 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) : CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 0) (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso B).hom (groupCohomology.shortComplexH0 B).f) = CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 A).f φ.hom)
• groupCohomology.H1π_comp_map_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) {Z : ModuleCat k} (h : groupCohomology B 1 ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.H1π A) (CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 1) h) = CategoryTheory.CategoryStruct.comp (groupCohomology.mapCocycles₁ f φ) (CategoryTheory.CategoryStruct.comp (groupCohomology.H1π B) h)
• groupCohomology.map_H0Iso_hom_f_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) {Z : ModuleCat k} (h : (groupCohomology.shortComplexH0 B).X₂ ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 0) (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso B).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 B).f h)) = CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 A).f (CategoryTheory.CategoryStruct.comp φ.hom h))
• groupCohomology.map_id_comp_H0Iso_hom_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B : Rep k G} (f : A ⟶ B) {Z : ModuleCat k} (h : ModuleCat.of k ↥B.ρ.invariants ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) f 0) (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso B).hom h) = CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom (CategoryTheory.CategoryStruct.comp ((Rep.invariantsFunctor k G).map f) h)
• groupCohomology.H2π_comp_map_assoc 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) {Z : ModuleCat k} (h : groupCohomology B 2 ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.H2π A) (CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 2) h) = CategoryTheory.CategoryStruct.comp (groupCohomology.mapCocycles₂ f φ) (CategoryTheory.CategoryStruct.comp (groupCohomology.H2π B) h)
• groupCohomology.map_id_comp_H0Iso_hom_apply 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G : Type u} [CommRing k] [Group G] {A B : Rep k G} (f : A ⟶ B) (x : CategoryTheory.ToType (groupCohomology A 0)) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.H0Iso B).hom) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.map (MonoidHom.id G) f 0)) x) = (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom ((Rep.invariantsFunctor k G).map f)) x
• groupCohomology.map_H0Iso_hom_f_apply 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (x : CategoryTheory.ToType (groupCohomology A 0)) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.shortComplexH0 B).f) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.H0Iso B).hom) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 0)) x)) = (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 A).f φ.hom)) x
• groupCohomology.H1π_comp_map_apply 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (x : CategoryTheory.ToType (ModuleCat.of k ↥(groupCohomology.cocycles₁ A))) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 1)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.H1π A)) x) = (CategoryTheory.ConcreteCategory.hom (groupCohomology.H1π B)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.mapCocycles₁ f φ)) x)
• groupCohomology.H2π_comp_map_apply 📋 Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
  {k G H : Type u} [CommRing k] [Group G] [Group H] {A : Rep k H} {B : Rep k G} (f : G →* H) (φ : (Action.res (ModuleCat k) f).obj A ⟶ B) (x : CategoryTheory.ToType (ModuleCat.of k ↥(groupCohomology.cocycles₂ A))) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 2)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.H2π A)) x) = (CategoryTheory.ConcreteCategory.hom (groupCohomology.H2π B)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.mapCocycles₂ f φ)) x)

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision ff04530 serving mathlib revision 8623f65