Theorems · Theorem · category theory

CategoryTheory.Presieve.IsSeparatedFor.isSheafFor

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
  {R : CategoryTheory.Presieve X},
  CategoryTheory.Presieve.IsSeparatedFor P R →
    (∀ (x : CategoryTheory.Presieve.FamilyOfElements P R), x.Compatible → ∃ t, x.IsAmalgamation t) →
      CategoryTheory.Presieve.IsSheafFor P R

If P is separated for R and every family has an amalgamation, then P is a sheaf for R.

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

1 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.Category