Loogle!

Result

Found 7 declarations mentioning CochainComplex.ConnectData.map.

• CochainComplex.ConnectData.map_id 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K : ChainComplex C ℕ} {L : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) : h.map h (CategoryTheory.CategoryStruct.id K) (CategoryTheory.CategoryStruct.id L) ⋯ = CategoryTheory.CategoryStruct.id h.cochainComplex
• CochainComplex.ConnectData.map 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K K' : ChainComplex C ℕ} {L L' : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) (h' : CochainComplex.ConnectData K' L') (fK : K ⟶ K') (fL : L ⟶ L') (f_comm : CategoryTheory.CategoryStruct.comp (fK.f 0) h'.d₀ = CategoryTheory.CategoryStruct.comp h.d₀ (fL.f 0)) : h.cochainComplex ⟶ h'.cochainComplex
• CochainComplex.ConnectData.map_f 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K K' : ChainComplex C ℕ} {L L' : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) (h' : CochainComplex.ConnectData K' L') (fK : K ⟶ K') (fL : L ⟶ L') (f_comm : CategoryTheory.CategoryStruct.comp (fK.f 0) h'.d₀ = CategoryTheory.CategoryStruct.comp h.d₀ (fL.f 0)) (x✝ : ℤ) : (h.map h' fK fL f_comm).f x✝ = match x✝ with | Int.ofNat n => fL.f n | Int.negSucc n => fK.f n
• CochainComplex.ConnectData.homologyMap_map_of_eq_succ 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K K' : ChainComplex C ℕ} {L L' : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) (h' : CochainComplex.ConnectData K' L') (fK : K ⟶ K') (fL : L ⟶ L') (f_comm : CategoryTheory.CategoryStruct.comp (fK.f 0) h'.d₀ = CategoryTheory.CategoryStruct.comp h.d₀ (fL.f 0)) (n : ℕ) [NeZero n] (m : ℤ) (hmn : m = ↑n) [HomologicalComplex.HasHomology h.cochainComplex m] [HomologicalComplex.HasHomology L n] [HomologicalComplex.HasHomology h'.cochainComplex m] [HomologicalComplex.HasHomology L' n] : HomologicalComplex.homologyMap (h.map h' fK fL f_comm) m = CategoryTheory.CategoryStruct.comp (h.homologyIsoPos n m hmn).hom (CategoryTheory.CategoryStruct.comp (HomologicalComplex.homologyMap fL n) (h'.homologyIsoPos n m hmn).inv)
• CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K K' : ChainComplex C ℕ} {L L' : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) (h' : CochainComplex.ConnectData K' L') (fK : K ⟶ K') (fL : L ⟶ L') (f_comm : CategoryTheory.CategoryStruct.comp (fK.f 0) h'.d₀ = CategoryTheory.CategoryStruct.comp h.d₀ (fL.f 0)) (n : ℕ) [NeZero n] (m : ℤ) (hmn : m = -↑(n + 1)) [HomologicalComplex.HasHomology h.cochainComplex m] [HomologicalComplex.HasHomology K n] [HomologicalComplex.HasHomology h'.cochainComplex m] [HomologicalComplex.HasHomology K' n] : HomologicalComplex.homologyMap (h.map h' fK fL f_comm) m = CategoryTheory.CategoryStruct.comp (h.homologyIsoNeg n m hmn).hom (CategoryTheory.CategoryStruct.comp (HomologicalComplex.homologyMap fK n) (h'.homologyIsoNeg n m hmn).inv)
• CochainComplex.ConnectData.map_comp_map 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K K' K'' : ChainComplex C ℕ} {L L' L'' : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) (h' : CochainComplex.ConnectData K' L') (h'' : CochainComplex.ConnectData K'' L'') (fK : K ⟶ K') (fL : L ⟶ L') (f_comm : CategoryTheory.CategoryStruct.comp (fK.f 0) h'.d₀ = CategoryTheory.CategoryStruct.comp h.d₀ (fL.f 0)) (fK' : K' ⟶ K'') (fL' : L' ⟶ L'') (f_comm' : CategoryTheory.CategoryStruct.comp (fK'.f 0) h''.d₀ = CategoryTheory.CategoryStruct.comp h'.d₀ (fL'.f 0)) : CategoryTheory.CategoryStruct.comp (h.map h' fK fL f_comm) (h'.map h'' fK' fL' f_comm') = h.map h'' (CategoryTheory.CategoryStruct.comp fK fK') (CategoryTheory.CategoryStruct.comp fL fL') ⋯
• CochainComplex.ConnectData.map.congr_simp 📋 Mathlib.Algebra.Homology.Embedding.Connect
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C] {K K' : ChainComplex C ℕ} {L L' : CochainComplex C ℕ} (h : CochainComplex.ConnectData K L) (h' : CochainComplex.ConnectData K' L') (fK fK✝ : K ⟶ K') (e_fK : fK = fK✝) (fL fL✝ : L ⟶ L') (e_fL : fL = fL✝) (f_comm : CategoryTheory.CategoryStruct.comp (fK.f 0) h'.d₀ = CategoryTheory.CategoryStruct.comp h.d₀ (fL.f 0)) : h.map h' fK fL f_comm = h.map h' fK✝ fL✝ ⋯

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 6ff4759 serving mathlib revision edaf32c