Theorems · Theorem · category theory

CategoryTheory.Presieve.isSheafFor_iff_generate

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

C2.1.3 in [Elephant]

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

20 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category