Theorems · Definition · category theory

CategoryTheory.Functor.map

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (self : CategoryTheory.Functor C D) → {X Y : C} → (X ⟶ Y) → (self.obj X ⟶ self.obj Y)

The action of a functor on morphisms.

Defined in

Mathlib.CategoryTheory.Functor.Basic

Cited by

8,698 results in Mathlib

Foundations

Depth 3 from the axioms, rests on 9 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category