Theorems · Theorem · category theory

CategoryTheory.Equalizer.Presieve.sheaf_condition

∀ {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.Presieve.IsSheafFor P R ↔
    Nonempty (CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.Fork.ofι (CategoryTheory.Equalizer.forkMap P R) ⋯))

P is a sheaf for R, iff the fork given by w is an equalizer.

Defined in

Mathlib.CategoryTheory.Sites.EqualizerSheafCondition

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Presieve.HasPairwisePullbacks