Loogle!

Result

Found 14 declarations mentioning groupCohomology.map.

• groupCohomology.functor_map 📋 Mathlib.RepresentationTheory.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.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.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.map_comp_isoH0_hom 📋 Mathlib.RepresentationTheory.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) (groupCohomology.isoH0 B).hom = CategoryTheory.CategoryStruct.comp (groupCohomology.isoH0 A).hom (groupCohomology.H0Map f φ)
• groupCohomology.map_comp_isoH1_hom 📋 Mathlib.RepresentationTheory.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 1) (groupCohomology.isoH1 B).hom = CategoryTheory.CategoryStruct.comp (groupCohomology.isoH1 A).hom (groupCohomology.H1Map f φ)
• groupCohomology.map_comp_isoH2_hom 📋 Mathlib.RepresentationTheory.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 2) (groupCohomology.isoH2 B).hom = CategoryTheory.CategoryStruct.comp (groupCohomology.isoH2 A).hom (groupCohomology.H2Map f φ)
• groupCohomology.map_id_comp 📋 Mathlib.RepresentationTheory.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_comp_isoH0_hom_assoc 📋 Mathlib.RepresentationTheory.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.H0 B ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 0) (CategoryTheory.CategoryStruct.comp (groupCohomology.isoH0 B).hom h) = CategoryTheory.CategoryStruct.comp (groupCohomology.isoH0 A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Map f φ) h)
• groupCohomology.map_comp_isoH1_hom_assoc 📋 Mathlib.RepresentationTheory.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.H1 B ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 1) (CategoryTheory.CategoryStruct.comp (groupCohomology.isoH1 B).hom h) = CategoryTheory.CategoryStruct.comp (groupCohomology.isoH1 A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.H1Map f φ) h)
• groupCohomology.map_comp_isoH2_hom_assoc 📋 Mathlib.RepresentationTheory.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.H2 B ⟶ Z) : CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 2) (CategoryTheory.CategoryStruct.comp (groupCohomology.isoH2 B).hom h) = CategoryTheory.CategoryStruct.comp (groupCohomology.isoH2 A).hom (CategoryTheory.CategoryStruct.comp (groupCohomology.H2Map f φ) h)
• groupCohomology.map_id_comp_assoc 📋 Mathlib.RepresentationTheory.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.map_comp_isoH0_hom_apply 📋 Mathlib.RepresentationTheory.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.isoH0 B).hom) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 0)) x) = (LinearMap.codRestrict B.ρ.invariants (ModuleCat.Hom.hom φ.hom ∘ₗ A.ρ.invariants.subtype) ⋯) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.isoH0 A).hom) x)
• groupCohomology.map_comp_isoH1_hom_apply 📋 Mathlib.RepresentationTheory.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 1)) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.isoH1 B).hom) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 1)) x) = (CategoryTheory.ConcreteCategory.hom (groupCohomology.H1Map f φ)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.isoH1 A).hom) x)
• groupCohomology.map_comp_isoH2_hom_apply 📋 Mathlib.RepresentationTheory.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 2)) : (CategoryTheory.ConcreteCategory.hom (groupCohomology.isoH2 B).hom) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 2)) x) = (CategoryTheory.ConcreteCategory.hom (groupCohomology.H2Map f φ)) ((CategoryTheory.ConcreteCategory.hom (groupCohomology.isoH2 A).hom) 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 19971e9 serving mathlib revision 40fea08