Loogle!

Result

Found 15 declarations mentioning CategoryTheory.StrictlyUnitaryPseudofunctorCore.map.

• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {X Y : B} : (X ⟶ Y) → (self.obj X ⟶ self.obj Y)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map_id 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) (X : B) : self.map (CategoryTheory.CategoryStruct.id X) = CategoryTheory.CategoryStruct.id (self.obj X)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.mapComp 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : self.map (CategoryTheory.CategoryStruct.comp f g) ≅ CategoryTheory.CategoryStruct.comp (self.map f) (self.map g)
• CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (S : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {X✝ Y✝ : B} (a✝ : X✝ ⟶ Y✝) : (CategoryTheory.StrictlyUnitaryPseudofunctor.mk' S).map a✝ = S.map a✝
• CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_mapComp 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (S : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a✝ b✝ c✝ : B} (f : a✝ ⟶ b✝) (g : b✝ ⟶ c✝) : (CategoryTheory.StrictlyUnitaryPseudofunctor.mk' S).mapComp f g = S.mapComp f g
• CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_mapId 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (S : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) (x : B) : (CategoryTheory.StrictlyUnitaryPseudofunctor.mk' S).mapId x = CategoryTheory.eqToIso ⋯
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂ 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b : B} {f g : a ⟶ b} : (f ⟶ g) → (self.map f ⟶ self.map g)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_id 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b : B} (f : a ⟶ b) : self.map₂ (CategoryTheory.CategoryStruct.id f) = CategoryTheory.CategoryStruct.id (self.map f)
• CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map₂ 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (S : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a✝ b✝ : B} {f✝ g✝ : a✝ ⟶ b✝} (a✝¹ : f✝ ⟶ g✝) : (CategoryTheory.StrictlyUnitaryPseudofunctor.mk' S).map₂ a✝¹ = S.map₂ a✝¹
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_comp 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h) : self.map₂ (CategoryTheory.CategoryStruct.comp η θ) = CategoryTheory.CategoryStruct.comp (self.map₂ η) (self.map₂ θ)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b c : B} (f : a ⟶ b) {g h : b ⟶ c} (η : g ⟶ h) : self.map₂ (CategoryTheory.Bicategory.whiskerLeft f η) = CategoryTheory.CategoryStruct.comp (self.mapComp f g).hom (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (self.map f) (self.map₂ η)) (self.mapComp f h).inv)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b c : B} {f g : a ⟶ b} (η : f ⟶ g) (h : b ⟶ c) : self.map₂ (CategoryTheory.Bicategory.whiskerRight η h) = CategoryTheory.CategoryStruct.comp (self.mapComp f h).hom (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (self.map₂ η) (self.map h)) (self.mapComp g h).inv)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b : B} (f : a ⟶ b) : self.map₂ (CategoryTheory.Bicategory.leftUnitor f).hom = CategoryTheory.CategoryStruct.comp (self.mapComp (CategoryTheory.CategoryStruct.id a) f).hom (CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯) (CategoryTheory.Bicategory.leftUnitor (self.map f)).hom)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b : B} (f : a ⟶ b) : self.map₂ (CategoryTheory.Bicategory.rightUnitor f).hom = CategoryTheory.CategoryStruct.comp (self.mapComp f (CategoryTheory.CategoryStruct.id b)).hom (CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯) (CategoryTheory.Bicategory.rightUnitor (self.map f)).hom)
• CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator 📋 Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
  {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.StrictlyUnitaryPseudofunctorCore B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) : self.map₂ (CategoryTheory.Bicategory.associator f g h).hom = CategoryTheory.CategoryStruct.comp (self.mapComp (CategoryTheory.CategoryStruct.comp f g) h).hom (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (self.mapComp f g).hom (self.map h)) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (self.map f) (self.map g) (self.map h)).hom (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (self.map f) (self.mapComp g h).inv) (self.mapComp f (CategoryTheory.CategoryStruct.comp g h)).inv)))

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