Loogle!

Result

Found 15 declarations mentioning CategoryTheory.Pseudofunctor.ObjectProperty.map.

• CategoryTheory.Pseudofunctor.ObjectProperty.map 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y : B} (f : X ⟶ Y) : CategoryTheory.Functor (P.Obj X) (P.Obj Y)
• CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X✝ Y✝ : B} (f : X✝ ⟶ Y✝) : (P.fullsubcategory.map f).toFunctor = P.map f
• CategoryTheory.Pseudofunctor.ObjectProperty.mapId 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] (X : B) : P.map (CategoryTheory.CategoryStruct.id X) ≅ CategoryTheory.Functor.id (P.Obj X)
• CategoryTheory.Pseudofunctor.ObjectProperty.mapComp 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y Z : B} (f : X ⟶ Y) (g : Y ⟶ Z) : P.map (CategoryTheory.CategoryStruct.comp f g) ≅ (P.map f).comp (P.map g)
• CategoryTheory.Pseudofunctor.ObjectProperty.map_obj_obj 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y : B} (f : X ⟶ Y) (X✝ : P.Obj X) : ((P.map f).obj X✝).obj = (F.map f).toFunctor.obj X✝.obj
• CategoryTheory.Pseudofunctor.ObjectProperty.map₂ 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y : B} {f g : X ⟶ Y} (α : f ⟶ g) : P.map f ⟶ P.map g
• CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {a✝ b✝ : B} {f✝ g✝ : a✝ ⟶ b✝} (α : f✝ ⟶ g✝) : (P.fullsubcategory.map₂ α).toNatTrans = P.map₂ α
• CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapId 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] (X : B) : P.fullsubcategory.mapId X = CategoryTheory.Cat.Hom.isoMk (P.mapId X)
• CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X : B} (M : P.Obj X) : (P.mapId X).hom.app M = CategoryTheory.ObjectProperty.homMk ((F.mapId X).hom.toNatTrans.app M.obj)
• CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X : B} (M : P.Obj X) : (P.mapId X).inv.app M = CategoryTheory.ObjectProperty.homMk ((F.mapId X).inv.toNatTrans.app M.obj)
• CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapComp 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {a✝ b✝ c✝ : B} (f : a✝ ⟶ b✝) (g : b✝ ⟶ c✝) : P.fullsubcategory.mapComp f g = CategoryTheory.Cat.Hom.isoMk (P.mapComp f g)
• CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y Z : B} (f : X ⟶ Y) (g : Y ⟶ Z) (M : P.Obj X) : (P.mapComp f g).hom.app M = CategoryTheory.ObjectProperty.homMk ((F.mapComp f g).hom.toNatTrans.app M.obj)
• CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y Z : B} (f : X ⟶ Y) (g : Y ⟶ Z) (M : P.Obj X) : (P.mapComp f g).inv.app M = CategoryTheory.ObjectProperty.homMk ((F.mapComp f g).inv.toNatTrans.app M.obj)
• CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y : B} (f : X ⟶ Y) {X✝ Y✝ : P.Obj X} (f✝ : X✝ ⟶ Y✝) : ((P.map f).map f✝).hom = (F.map f).toFunctor.map f✝.hom
• CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom 📋 Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty
  {B : Type u} [CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat} (P : F.ObjectProperty) [P.IsClosedUnderMapObj] {X Y : B} {f g : X ⟶ Y} (α : f ⟶ g) (X✝ : P.Obj X) : ((P.map₂ α).app X✝).hom = (F.map₂ α).toNatTrans.app X✝.obj

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 36960b0 serving mathlib revision 9a4cf1d