Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.CoGrothendieck.mapIdIso

{𝒮 : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} 𝒮] →
    (F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat) →
      CategoryTheory.Pseudofunctor.CoGrothendieck.map (CategoryTheory.CategoryStruct.id F) ≅
        CategoryTheory.Functor.id F.CoGrothendieck

The natural isomorphism witnessing the pseudo-unity constraint of CoGrothendieck.map.

Defined in: Mathlib.CategoryTheory.Bicategory.Grothendieck
Cited by: 1 results in Mathlib
Foundations: Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.CategoryStruct.idstatement · cited by 6,235
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.Catstatement and proof · cited by 884
CategoryTheory.Pseudofunctorstatement and proof · cited by 571
CategoryTheory.LocallyDiscretestatement and proof · cited by 318
CategoryTheory.NatIso.ofComponentsproof · cited by 178
CategoryTheory.Pseudofunctor.StrongTrans.categoryStructstatement · cited by 112
CategoryTheory.eqToIsoproof · cited by 97

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_eqproof · cited by 0