Loogle!

Result

Found 12 declarations mentioning CategoryTheory.Sigma.map.

• CategoryTheory.Sigma.map 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} (g : J → I) : CategoryTheory.Functor ((j : J) × C (g j)) ((i : I) × C i)
• CategoryTheory.Sigma.mapId 📋 Mathlib.CategoryTheory.Sigma.Basic
  (I : Type w₁) (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] : CategoryTheory.Sigma.map C id ≅ CategoryTheory.Functor.id ((i : I) × C i)
• CategoryTheory.Sigma.inclCompMap 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} (g : J → I) (j : J) : (CategoryTheory.Sigma.incl j).comp (CategoryTheory.Sigma.map C g) ≅ CategoryTheory.Sigma.incl (g j)
• CategoryTheory.Sigma.map_obj 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} (g : J → I) (j : J) (X : C (g j)) : (CategoryTheory.Sigma.map C g).obj ⟨j, X⟩ = ⟨g j, X⟩
• CategoryTheory.Sigma.mapComp 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} {K : Type w₃} (f : K → J) (g : J → I) : (CategoryTheory.Sigma.map (fun x => C (g x)) f).comp (CategoryTheory.Sigma.map C g) ≅ CategoryTheory.Sigma.map C (g ∘ f)
• CategoryTheory.Sigma.map_map 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} (g : J → I) {j : J} {X Y : C (g j)} (f : X ⟶ Y) : (CategoryTheory.Sigma.map C g).map (CategoryTheory.Sigma.SigmaHom.mk f) = CategoryTheory.Sigma.SigmaHom.mk f
• CategoryTheory.Sigma.mapId_hom_app 📋 Mathlib.CategoryTheory.Sigma.Basic
  (I : Type w₁) (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] (x✝ : (i : I) × (fun i => C (id i)) i) : (CategoryTheory.Sigma.mapId I C).hom.app x✝ = CategoryTheory.CategoryStruct.id ⟨x✝.fst, x✝.snd⟩
• CategoryTheory.Sigma.mapId_inv_app 📋 Mathlib.CategoryTheory.Sigma.Basic
  (I : Type w₁) (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] (x✝ : (i : I) × (fun i => C (id i)) i) : (CategoryTheory.Sigma.mapId I C).inv.app x✝ = CategoryTheory.CategoryStruct.id ⟨x✝.fst, x✝.snd⟩
• CategoryTheory.Sigma.inclCompMap_hom_app 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} (g : J → I) (j : J) (X : C (g j)) : (CategoryTheory.Sigma.inclCompMap C g j).hom.app X = CategoryTheory.CategoryStruct.id ⟨g j, X⟩
• CategoryTheory.Sigma.inclCompMap_inv_app 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} (g : J → I) (j : J) (X : C (g j)) : (CategoryTheory.Sigma.inclCompMap C g j).inv.app X = CategoryTheory.CategoryStruct.id ⟨g j, X⟩
• CategoryTheory.Sigma.mapComp_hom_app 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} {K : Type w₃} (f : K → J) (g : J → I) (X : (i : K) × (fun i => C (g (f i))) i) : (CategoryTheory.Sigma.mapComp C f g).hom.app X = CategoryTheory.CategoryStruct.id ⟨g (f X.fst), X.snd⟩
• CategoryTheory.Sigma.mapComp_inv_app 📋 Mathlib.CategoryTheory.Sigma.Basic
  {I : Type w₁} (C : I → Type u₁) [(i : I) → CategoryTheory.Category.{v₁, u₁} (C i)] {J : Type w₂} {K : Type w₃} (f : K → J) (g : J → I) (X : (i : K) × (fun i => C (g (f i))) i) : (CategoryTheory.Sigma.mapComp C f g).inv.app X = CategoryTheory.CategoryStruct.id ⟨g (f X.fst), X.snd⟩

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