Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso

{𝒮 : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} 𝒮] →
    {F G H : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮) 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)

The natural isomorphism witnessing the pseudo-functoriality of Grothendieck.map.

Defined in

Mathlib.CategoryTheory.Bicategory.Grothendieck

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category