Theorems · Theorem · category theory

CategoryTheory.Functor.map_comp

∀ {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 Z : C} (f : X ⟶ Y) (g : Y ⟶ Z),
  self.map (CategoryTheory.CategoryStruct.comp f g) = CategoryTheory.CategoryStruct.comp (self.map f) (self.map g)

A functor preserves composition.

Defined in

Mathlib.CategoryTheory.Functor.Basic

Cited by

734 results in Mathlib

Foundations

Depth 4 from the axioms, rests on 11 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category