Loogle!

Result

Found 9 declarations mentioning CochainComplex.HomComplex.Cochain.map.

• CochainComplex.HomComplex.Cochain.map 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {K L : CochainComplex C ℤ} {n : ℤ} {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (z : CochainComplex.HomComplex.Cochain K L n) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : CochainComplex.HomComplex.Cochain ((Φ.mapHomologicalComplex (ComplexShape.up ℤ)).obj K) ((Φ.mapHomologicalComplex (ComplexShape.up ℤ)).obj L) n
• CochainComplex.HomComplex.δ_map 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {K L : CochainComplex C ℤ} (n m : ℤ) {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (z : CochainComplex.HomComplex.Cochain K L n) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : CochainComplex.HomComplex.δ n m (z.map Φ) = (CochainComplex.HomComplex.δ n m z).map Φ
• CochainComplex.HomComplex.Cochain.map_v 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {K L : CochainComplex C ℤ} {n : ℤ} {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (z : CochainComplex.HomComplex.Cochain K L n) (Φ : CategoryTheory.Functor C D) [Φ.Additive] (p q : ℤ) (hpq : p + n = q) : (z.map Φ).v p q hpq = Φ.map (z.v p q hpq)
• CochainComplex.HomComplex.Cochain.map_comp 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {F G : CochainComplex C ℤ} (K : CochainComplex C ℤ) {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] {n₁ n₂ n₁₂ : ℤ} (z₁ : CochainComplex.HomComplex.Cochain F G n₁) (z₂ : CochainComplex.HomComplex.Cochain G K n₂) (h : n₁ + n₂ = n₁₂) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : (z₁.comp z₂ h).map Φ = (z₁.map Φ).comp (z₂.map Φ) h
• CochainComplex.HomComplex.Cochain.map_ofHom 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] (K L : CochainComplex C ℤ) {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (f : K ⟶ L) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : (CochainComplex.HomComplex.Cochain.ofHom f).map Φ = CochainComplex.HomComplex.Cochain.ofHom ((Φ.mapHomologicalComplex (ComplexShape.up ℤ)).map f)
• CochainComplex.HomComplex.Cochain.map_neg 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {K L : CochainComplex C ℤ} {n : ℤ} {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (z : CochainComplex.HomComplex.Cochain K L n) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : (-z).map Φ = -z.map Φ
• CochainComplex.HomComplex.Cochain.map_zero 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] (K L : CochainComplex C ℤ) (n : ℤ) {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (Φ : CategoryTheory.Functor C D) [Φ.Additive] : CochainComplex.HomComplex.Cochain.map 0 Φ = 0
• CochainComplex.HomComplex.Cochain.map_sub 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {K L : CochainComplex C ℤ} {n : ℤ} {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (z z' : CochainComplex.HomComplex.Cochain K L n) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : (z - z').map Φ = z.map Φ - z'.map Φ
• CochainComplex.HomComplex.Cochain.map_add 📋 Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
  {C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Preadditive C] {K L : CochainComplex C ℤ} {n : ℤ} {D : Type u_2} [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive D] (z z' : CochainComplex.HomComplex.Cochain K L n) (Φ : CategoryTheory.Functor C D) [Φ.Additive] : (z + z').map Φ = z.map Φ + z'.map Φ

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 bce1d65