Theorems · Theorem · category theory

CategoryTheory.Equalizer.Presieve.Arrows.w

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.Functor Cᵒᵖ (Type w)) {B : C} {I : Type t}
  [inst_1 : Small.{w, t} I] (X : I → C) (π : (i : I) → X i ⟶ B)
  [inst_2 : (CategoryTheory.Presieve.ofArrows X π).HasPairwisePullbacks],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Equalizer.Presieve.Arrows.forkMap P X π)
      (CategoryTheory.Equalizer.Presieve.Arrows.firstMap P X π) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Equalizer.Presieve.Arrows.forkMap P X π)
      (CategoryTheory.Equalizer.Presieve.Arrows.secondMap P X π)

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.CategorySmallCategoryTheory.Presieve.HasPairwisePullbacks