Theorems · Theorem · category theory

CategoryTheory.Equalizer.Presieve.w

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.Functor Cᵒᵖ (Type (max v u))) {X : C}
  (R : CategoryTheory.Presieve X) [inst_1 : R.HasPairwisePullbacks],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Equalizer.forkMap P R)
      (CategoryTheory.Equalizer.Presieve.firstMap P R) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Equalizer.forkMap P R)
      (CategoryTheory.Equalizer.Presieve.secondMap P R)

Defined in

Mathlib.CategoryTheory.Sites.EqualizerSheafCondition

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Presieve.HasPairwisePullbacks