Theorems · Theorem · category theory

CategoryTheory.Limits.pullback_equalizer

∀ {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) [inst_2 : CategoryTheory.Limits.HasPullbacks C],
  (CategoryTheory.Subobject.pullback h).obj (CategoryTheory.Limits.equalizerSubobject f g) =
    CategoryTheory.Limits.equalizerSubobject (CategoryTheory.CategoryStruct.comp h f)
      (CategoryTheory.CategoryStruct.comp h g)

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasEqualizerCategoryTheory.Limits.HasPullbacks