Theorems · Theorem · category theory

CategoryTheory.Limits.equalizerSubobject_factors_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f g : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasEqualizer f g] {W : C} (h : W ⟶ X),
  (CategoryTheory.Limits.equalizerSubobject f g).Factors h ↔
    CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp h g

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasEqualizer