Loogle!

Result

Found 14 declarations mentioning CategoryTheory.Pseudofunctor.Grothendieck.map.

• CategoryTheory.Pseudofunctor.Grothendieck.map_id_eq 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] (F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat) : CategoryTheory.Pseudofunctor.Grothendieck.map (CategoryTheory.CategoryStruct.id F) = CategoryTheory.Functor.id F.Grothendieck
• CategoryTheory.Pseudofunctor.Grothendieck.map 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) : CategoryTheory.Functor F.Grothendieck G.Grothendieck
• CategoryTheory.Pseudofunctor.Grothendieck.mapIdIso 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] (F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat) : CategoryTheory.Pseudofunctor.Grothendieck.map (CategoryTheory.CategoryStruct.id F) ≅ CategoryTheory.Functor.id F.Grothendieck
• CategoryTheory.Pseudofunctor.Grothendieck.map_comp_forget 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) : (CategoryTheory.Pseudofunctor.Grothendieck.map α).comp (CategoryTheory.Pseudofunctor.Grothendieck.forget G) = CategoryTheory.Pseudofunctor.Grothendieck.forget F
• CategoryTheory.Pseudofunctor.Grothendieck.map_obj_base 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) (a : F.Grothendieck) : ((CategoryTheory.Pseudofunctor.Grothendieck.map α).obj a).base = a.base
• CategoryTheory.Pseudofunctor.Grothendieck.map_comp_eq 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G H : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) (β : G ⟶ H) : CategoryTheory.Pseudofunctor.Grothendieck.map (CategoryTheory.CategoryStruct.comp α β) = (CategoryTheory.Pseudofunctor.Grothendieck.map α).comp (CategoryTheory.Pseudofunctor.Grothendieck.map β)
• CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G H : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) (β : G ⟶ H) : CategoryTheory.Pseudofunctor.Grothendieck.map (CategoryTheory.CategoryStruct.comp α β) ≅ (CategoryTheory.Pseudofunctor.Grothendieck.map α).comp (CategoryTheory.Pseudofunctor.Grothendieck.map β)
• CategoryTheory.Pseudofunctor.Grothendieck.map_id_map 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} {x y : F.Grothendieck} (f : x ⟶ y) : (CategoryTheory.Pseudofunctor.Grothendieck.map (CategoryTheory.CategoryStruct.id F)).map f = f
• CategoryTheory.Pseudofunctor.Grothendieck.mapIdIso.eq_1 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] (F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat) : CategoryTheory.Pseudofunctor.Grothendieck.mapIdIso F = CategoryTheory.NatIso.ofComponents (fun x => CategoryTheory.eqToIso ⋯) ⋯
• CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso.eq_1 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G H : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) (β : G ⟶ H) : CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso α β = CategoryTheory.NatIso.ofComponents (fun x => CategoryTheory.eqToIso ⋯) ⋯
• CategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) (a : F.Grothendieck) : ((CategoryTheory.Pseudofunctor.Grothendieck.map α).obj a).fiber = (α.app { as := Opposite.op a.base }).obj a.fiber
• CategoryTheory.Pseudofunctor.Grothendieck.map_map_base 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) {a b : F.Grothendieck} (f : a ⟶ b) : ((CategoryTheory.Pseudofunctor.Grothendieck.map α).map f).base = f.base
• CategoryTheory.Pseudofunctor.Grothendieck.map.eq_1 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) : CategoryTheory.Pseudofunctor.Grothendieck.map α = { obj := fun a => { base := a.base, fiber := (α.app { as := Opposite.op a.base }).obj a.fiber }, map := fun {a b} f => { base := f.base, fiber := CategoryTheory.CategoryStruct.comp ((α.app { as := Opposite.op a.base }).map f.fiber) ((α.naturality f.base.op.toLoc).hom.app b.fiber) }, map_id := ⋯, map_comp := ⋯ }
• CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber 📋 Mathlib.CategoryTheory.Bicategory.Grothendieck
  {𝒮 : Type u₁} [CategoryTheory.Category.{v₁, u₁} 𝒮] {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} (α : F ⟶ G) {a b : F.Grothendieck} (f : a ⟶ b) : ((CategoryTheory.Pseudofunctor.Grothendieck.map α).map f).fiber = CategoryTheory.CategoryStruct.comp ((α.app { as := Opposite.op a.base }).map f.fiber) ((α.naturality f.base.op.toLoc).hom.app b.fiber)

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 ff04530 serving mathlib revision 8623f65