Loogle!

Result

Found 18 declarations mentioning CategoryTheory.StructuredArrow.map.

• CategoryTheory.StructuredArrow.map 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {T : CategoryTheory.Functor C D} (f : S ⟶ S') : CategoryTheory.Functor (CategoryTheory.StructuredArrow S' T) (CategoryTheory.StructuredArrow S T)
• CategoryTheory.StructuredArrow.map_id 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S : D} {T : CategoryTheory.Functor C D} {f : CategoryTheory.StructuredArrow S T} : (CategoryTheory.StructuredArrow.map (CategoryTheory.CategoryStruct.id S)).obj f = f
• CategoryTheory.StructuredArrow.map_obj_right 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {T : CategoryTheory.Functor C D} (f : S ⟶ S') (X : CategoryTheory.Comma (CategoryTheory.Functor.fromPUnit S') T) : ((CategoryTheory.StructuredArrow.map f).obj X).right = X.right
• CategoryTheory.StructuredArrow.map_obj_left 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {T : CategoryTheory.Functor C D} (f : S ⟶ S') (X : CategoryTheory.Comma (CategoryTheory.Functor.fromPUnit S') T) : ((CategoryTheory.StructuredArrow.map f).obj X).left = X.left
• CategoryTheory.StructuredArrow.map_mk 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {Y : C} {T : CategoryTheory.Functor C D} {f : S' ⟶ T.obj Y} (g : S ⟶ S') : (CategoryTheory.StructuredArrow.map g).obj (CategoryTheory.StructuredArrow.mk f) = CategoryTheory.StructuredArrow.mk (CategoryTheory.CategoryStruct.comp g f)
• CategoryTheory.StructuredArrow.mapIsoMap₂ 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {T : CategoryTheory.Functor C D} {S S' : D} (f : S ⟶ S') : CategoryTheory.StructuredArrow.map f ≅ CategoryTheory.StructuredArrow.map₂ f (CategoryTheory.CategoryStruct.id T)
• CategoryTheory.StructuredArrow.map_comp 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' S'' : D} {T : CategoryTheory.Functor C D} {f : S ⟶ S'} {f' : S' ⟶ S''} {h : CategoryTheory.StructuredArrow S'' T} : (CategoryTheory.StructuredArrow.map (CategoryTheory.CategoryStruct.comp f f')).obj h = (CategoryTheory.StructuredArrow.map f).obj ((CategoryTheory.StructuredArrow.map f').obj h)
• CategoryTheory.StructuredArrow.map_obj_hom 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {T : CategoryTheory.Functor C D} (f : S ⟶ S') (X : CategoryTheory.Comma (CategoryTheory.Functor.fromPUnit S') T) : ((CategoryTheory.StructuredArrow.map f).obj X).hom = CategoryTheory.CategoryStruct.comp f X.hom
• CategoryTheory.StructuredArrow.map_map_right 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {T : CategoryTheory.Functor C D} (f : S ⟶ S') {X✝ Y✝ : CategoryTheory.Comma (CategoryTheory.Functor.fromPUnit S') T} (f✝ : X✝ ⟶ Y✝) : ((CategoryTheory.StructuredArrow.map f).map f✝).right = f✝.right
• CategoryTheory.StructuredArrow.map_map_left 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S S' : D} {T : CategoryTheory.Functor C D} (f : S ⟶ S') {X✝ Y✝ : CategoryTheory.Comma (CategoryTheory.Functor.fromPUnit S') T} (f✝ : X✝ ⟶ Y✝) : ((CategoryTheory.StructuredArrow.map f).map f✝).left = CategoryTheory.CategoryStruct.id X✝.left
• CategoryTheory.Limits.Cone.toStructuredArrowCone 📋 Mathlib.CategoryTheory.Limits.ConeCategory
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {D : Type u₄} [CategoryTheory.Category.{v₄, u₄} D] {K : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cone K) (F : CategoryTheory.Functor C D) {X : D} (f : X ⟶ F.obj c.pt) : CategoryTheory.Limits.Cone ((F.mapCone c).toStructuredArrow.comp ((CategoryTheory.StructuredArrow.map f).comp (CategoryTheory.StructuredArrow.pre X K F)))
• CategoryTheory.Limits.Cone.toStructuredArrowCone_pt 📋 Mathlib.CategoryTheory.Limits.ConeCategory
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {D : Type u₄} [CategoryTheory.Category.{v₄, u₄} D] {K : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cone K) (F : CategoryTheory.Functor C D) {X : D} (f : X ⟶ F.obj c.pt) : (c.toStructuredArrowCone F f).pt = CategoryTheory.StructuredArrow.mk f
• CategoryTheory.Limits.Cone.toStructuredArrowCone_π_app 📋 Mathlib.CategoryTheory.Limits.ConeCategory
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {D : Type u₄} [CategoryTheory.Category.{v₄, u₄} D] {K : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cone K) (F : CategoryTheory.Functor C D) {X : D} (f : X ⟶ F.obj c.pt) (j : J) : (c.toStructuredArrowCone F f).π.app j = CategoryTheory.StructuredArrow.homMk (c.π.app j) ⋯
• CategoryTheory.Functor.LeftExtension.precomp₂_map_right 📋 Mathlib.CategoryTheory.Functor.KanExtension.Basic
  {C : Type u_1} {H : Type u_3} {D : Type u_4} {D' : Type u_5} [CategoryTheory.Category.{u_6, u_1} C] [CategoryTheory.Category.{u_7, u_3} H] [CategoryTheory.Category.{u_8, u_4} D] [CategoryTheory.Category.{u_9, u_5} D'] {F₀ : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D} {F₁ : CategoryTheory.Functor D H} (L' : CategoryTheory.Functor D D') (α : F₀ ⟶ L.comp F₁) {X✝ Y✝ : L'.LeftExtension F₁} (f : X✝ ⟶ Y✝) : ((CategoryTheory.Functor.LeftExtension.precomp₂ L' α).map f).right = f.right
• CategoryTheory.Functor.LeftExtension.precomp₂_map_left 📋 Mathlib.CategoryTheory.Functor.KanExtension.Basic
  {C : Type u_1} {H : Type u_3} {D : Type u_4} {D' : Type u_5} [CategoryTheory.Category.{u_6, u_1} C] [CategoryTheory.Category.{u_7, u_3} H] [CategoryTheory.Category.{u_8, u_4} D] [CategoryTheory.Category.{u_9, u_5} D'] {F₀ : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D} {F₁ : CategoryTheory.Functor D H} (L' : CategoryTheory.Functor D D') (α : F₀ ⟶ L.comp F₁) {X✝ Y✝ : L'.LeftExtension F₁} (f : X✝ ⟶ Y✝) : ((CategoryTheory.Functor.LeftExtension.precomp₂ L' α).map f).left = CategoryTheory.CategoryStruct.id X✝.left
• CategoryTheory.Functor.pointwiseRightKanExtension_map 📋 Mathlib.CategoryTheory.Functor.KanExtension.Pointwise
  {C : Type u_1} {D : Type u_2} {H : Type u_4} [CategoryTheory.Category.{u_5, u_1} C] [CategoryTheory.Category.{u_6, u_2} D] [CategoryTheory.Category.{u_7, u_4} H] (L : CategoryTheory.Functor C D) (F : CategoryTheory.Functor C H) [L.HasPointwiseRightKanExtension F] {Y₁ Y₂ : D} (f : Y₁ ⟶ Y₂) : (L.pointwiseRightKanExtension F).map f = CategoryTheory.Limits.limit.lift ((CategoryTheory.StructuredArrow.proj Y₂ L).comp F) { pt := CategoryTheory.Limits.limit ((CategoryTheory.StructuredArrow.proj Y₁ L).comp F), π := { app := fun g => CategoryTheory.Limits.limit.π ((CategoryTheory.StructuredArrow.proj Y₁ L).comp F) ((CategoryTheory.StructuredArrow.map f).obj g), naturality := ⋯ } }
• CategoryTheory.StructuredArrow.functor_map 📋 Mathlib.CategoryTheory.Comma.StructuredArrow.Functor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (T : CategoryTheory.Functor C D) {X✝ Y✝ : Dᵒᵖ} (f : X✝ ⟶ Y✝) : (CategoryTheory.StructuredArrow.functor T).map f = CategoryTheory.StructuredArrow.map f.unop
• CategoryTheory.StructuredArrow.final_map 📋 Mathlib.CategoryTheory.Filtered.Final
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] [CategoryTheory.IsFiltered C] {S S' : D} (f : S ⟶ S') (T : CategoryTheory.Functor C D) [T.Final] : (CategoryTheory.StructuredArrow.map f).Final

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 ee8c038 serving mathlib revision 7a9e177