Loogle!

Result

Found 4 declarations mentioning CategoryTheory.Functorial.map.

• CategoryTheory.Functorial.map 📋 Mathlib.CategoryTheory.Functor.Functorial
  {C : Type u₁} {inst✝ : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst✝¹ : CategoryTheory.Category.{v₂, u₂} D} (F : C → D) [self : CategoryTheory.Functorial F] {X Y : C} : (X ⟶ Y) → (F X ⟶ F Y)
• CategoryTheory.Functorial.map_id 📋 Mathlib.CategoryTheory.Functor.Functorial
  {C : Type u₁} {inst✝ : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst✝¹ : CategoryTheory.Category.{v₂, u₂} D} {F : C → D} [self : CategoryTheory.Functorial F] {X : C} : CategoryTheory.map F (CategoryTheory.CategoryStruct.id X) = CategoryTheory.CategoryStruct.id (F X)
• CategoryTheory.Functorial.map_comp 📋 Mathlib.CategoryTheory.Functor.Functorial
  {C : Type u₁} {inst✝ : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst✝¹ : CategoryTheory.Category.{v₂, u₂} D} {F : C → D} [self : CategoryTheory.Functorial F] {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z} : CategoryTheory.map F (CategoryTheory.CategoryStruct.comp f g) = CategoryTheory.CategoryStruct.comp (CategoryTheory.map F f) (CategoryTheory.map F g)
• CategoryTheory.map_functorial_obj 📋 Mathlib.CategoryTheory.Functor.Functorial
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y) : CategoryTheory.map F.obj f = F.map f

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