Theorems · Definition · category theory

CategoryTheory.Grothendieck.preUnitIso

{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.map (CategoryTheory.Functor.whiskerRight G.unitInv (G.functor.comp F)) ≅
              CategoryTheory.Grothendieck.pre (G.functor.comp F) (G.functor.comp G.inverse)

Let G be an equivalence of categories. The functor induced via pre by G.functor ⋙ G.inverse is naturally isomorphic to the functor induced via map by a whiskered version of G's inverse unit.

Defined in

Mathlib.CategoryTheory.Grothendieck

Cited by

0 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category