Loogle!

Result

Found 89 declarations mentioning Quiver.Hom and CategoryTheory.ShortComplex.Exact. Of these, 4 match your pattern(s).

• CategoryTheory.ShortComplex.Exact.desc 📋 Mathlib.Algebra.Homology.ShortComplex.Exact
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Preadditive C] {S : CategoryTheory.ShortComplex C} [CategoryTheory.Balanced C] (hS : S.Exact) {A : C} (k : S.X₂ ⟶ A) (hk : CategoryTheory.CategoryStruct.comp S.f k = 0) [CategoryTheory.Epi S.g] : S.X₃ ⟶ A
• CategoryTheory.ShortComplex.Exact.lift 📋 Mathlib.Algebra.Homology.ShortComplex.Exact
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Preadditive C] {S : CategoryTheory.ShortComplex C} [CategoryTheory.Balanced C] (hS : S.Exact) {A : C} (k : A ⟶ S.X₂) (hk : CategoryTheory.CategoryStruct.comp k S.g = 0) [CategoryTheory.Mono S.f] : A ⟶ S.X₁
• CategoryTheory.ShortComplex.Exact.descToInjective 📋 Mathlib.Algebra.Homology.ShortComplex.Exact
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Abelian C] {S : CategoryTheory.ShortComplex C} (hS : S.Exact) {J : C} (f : S.X₂ ⟶ J) [CategoryTheory.Injective J] (hf : CategoryTheory.CategoryStruct.comp S.f f = 0) : S.X₃ ⟶ J
• CategoryTheory.ShortComplex.Exact.liftFromProjective 📋 Mathlib.Algebra.Homology.ShortComplex.Exact
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Abelian C] {S : CategoryTheory.ShortComplex C} (hS : S.Exact) {P : C} (f : P ⟶ S.X₂) [CategoryTheory.Projective P] (hf : CategoryTheory.CategoryStruct.comp f S.g = 0) : P ⟶ S.X₁

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 abad10c