Theorems · Definition · category theory

CategoryTheory.CoreSmallCategoryOfSet.arrowEquiv

{Ω : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (h : CategoryTheory.CoreSmallCategoryOfSet Ω C) →
        CategoryTheory.Arrow ↑h.smallCategoryOfSet.obj ≃ CategoryTheory.Arrow C

Given h : CoreSmallCategoryOfSet Ω C, the equivalence of categories h.smallCategoryOfSet.obj ≌ C is actually an isomorphism: it induces a bijection on the type of arrows.

Defined in

Mathlib.CategoryTheory.SmallRepresentatives

Cited by

1 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category