Theorems · Definition · category theory

CategoryTheory.Functor.op

{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 Cᵒᵖ Dᵒᵖ

The opposite of a functor, i.e. considering a functor F : C ⥤ D as a functor Cᵒᵖ ⥤ Dᵒᵖ. In informal mathematics no distinction is made between these.

Defined in

Mathlib.CategoryTheory.Opposites

Cited by

997 results in Mathlib

Foundations

Depth 12 from the axioms, rests on 59 definitions · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.Category