Theorems · Theorem · category theory

CategoryTheory.Presieve.isSheafFor_iso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
  {R : CategoryTheory.Presieve X} {P' : CategoryTheory.Functor Cᵒᵖ (Type w)} (i : P ≅ P'),
  CategoryTheory.Presieve.IsSheafFor P R → CategoryTheory.Presieve.IsSheafFor P' R

If P is a sheaf for S, and it is iso to P', then P' is a sheaf for S. This shows that "being a sheaf for a presieve" is a mathematical or hygienic property.

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

3 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category