Theorems · Theorem · category theory

CategoryTheory.id_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type w}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {X : C}
  (x : CategoryTheory.ToType X), (CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.id X)) x = x

Defined in

Mathlib.CategoryTheory.ConcreteCategory.Basic

Cited by

100 results in Mathlib

Foundations

Depth 6 from the axioms, rests on 18 definitions · uses propext

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory