Theorems · Definition · category theory

CategoryTheory.Functor.mapArrow

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        CategoryTheory.Functor C D → CategoryTheory.Functor (CategoryTheory.Arrow C) (CategoryTheory.Arrow D)

A functor C ⥤ D induces a functor between the corresponding arrow categories.

Defined in

Mathlib.CategoryTheory.Comma.Arrow

Cited by

31 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category