Theorems · Definition · category theory

CategoryTheory.Arrow.isoOfNatIso

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {F G : CategoryTheory.Functor C D} →
          (F ≅ G) → (f : CategoryTheory.Arrow C) → F.mapArrow.obj f ≅ G.mapArrow.obj f

The images of f : Arrow C by two isomorphic functors F : C ⥤ D are isomorphic arrows in D.

Defined in

Mathlib.CategoryTheory.Comma.Arrow

Cited by

7 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category