Theorems · Theorem · category theory

CategoryTheory.Presieve.isSheafFor_iff_yonedaSheafCondition

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {S : CategoryTheory.Sieve X}
  {P : CategoryTheory.Functor Cᵒᵖ (Type v₁)},
  CategoryTheory.Presieve.IsSheafFor P S.arrows ↔ CategoryTheory.Presieve.YonedaSheafCondition P S

The yoneda version of the sheaf condition is equivalent to the sheaf condition. C2.1.4 of [Elephant].

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category