Theorems · Theorem · category theory

CategoryTheory.Functor.map_id

∀ {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 : C),
  self.map (CategoryTheory.CategoryStruct.id X) = CategoryTheory.CategoryStruct.id (self.obj X)

A functor preserves identity morphisms.

Defined in

Mathlib.CategoryTheory.Functor.Basic

Cited by

616 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category