Theorems · Definition · category theory

CategoryTheory.Limits.equalizerSubobjectIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      (f g : X ⟶ Y) →
        [inst_1 : CategoryTheory.Limits.HasEqualizer f g] →
          CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.equalizerSubobject f g) ≅
            CategoryTheory.Limits.equalizer f g

The underlying object of equalizerSubobject f g is (up to isomorphism!) the same as the chosen object equalizer f g.

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

5 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasEqualizer