Theorems · Definition · category theory

CategoryTheory.Grothendieck.preEquivalence

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} D] →
        (F : CategoryTheory.Functor C CategoryTheory.Cat) →
          (G : D ≌ C) → CategoryTheory.Grothendieck (G.functor.comp F) ≌ CategoryTheory.Grothendieck F

Given a functor F : C ⥤ Cat and an equivalence of categories G : D ≌ C, the functor pre F G.functor is an equivalence between Grothendieck (G.functor ⋙ F) and Grothendieck F.

Defined in

Mathlib.CategoryTheory.Grothendieck

Cited by

1 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category