Loogle!

Result

Found 8 declarations mentioning CategoryTheory.GrothendieckTopology.Cover.Arrow.map.

• CategoryTheory.GrothendieckTopology.Cover.Arrow.map 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} (I : S.Arrow) (f : S ⟶ T) : T.Arrow
• CategoryTheory.GrothendieckTopology.Cover.Arrow.map_Y 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} (I : S.Arrow) (f : S ⟶ T) : (I.map f).Y = I.Y
• CategoryTheory.GrothendieckTopology.Cover.Arrow.map_f 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} (I : S.Arrow) (f : S ⟶ T) : (I.map f).f = I.f
• CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.map 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} {I₁ I₂ : S.Arrow} (r : I₁.Relation I₂) (f : S ⟶ T) : (I₁.map f).Relation (I₂.map f)
• CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.map_Z 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} {I₁ I₂ : S.Arrow} (r : I₁.Relation I₂) (f : S ⟶ T) : (r.map f).Z = r.Z
• CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.map_g₁ 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} {I₁ I₂ : S.Arrow} (r : I₁.Relation I₂) (f : S ⟶ T) : (r.map f).g₁ = r.g₁
• CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.map_g₂ 📋 Mathlib.CategoryTheory.Sites.Grothendieck
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C} {S T : J.Cover X} {I₁ I₂ : S.Arrow} (r : I₁.Relation I₂) (f : S ⟶ T) : (r.map f).g₂ = r.g₂
• CategoryTheory.GrothendieckTopology.diagram_map 📋 Mathlib.CategoryTheory.Sites.Plus
  {C : Type u} [CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type w} [CategoryTheory.Category.{max v u, w} D] [∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X), CategoryTheory.Limits.HasMultiequalizer (S.index P)] (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) {S x✝ : (J.Cover X)ᵒᵖ} (f : S ⟶ x✝) : (J.diagram P X).map f = CategoryTheory.Limits.Multiequalizer.lift ((Opposite.unop x✝).index P) (CategoryTheory.Limits.multiequalizer ((Opposite.unop S).index P)) (fun I => CategoryTheory.Limits.Multiequalizer.ι ((Opposite.unop S).index P) (CategoryTheory.GrothendieckTopology.Cover.Arrow.map I f.unop)) ⋯

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