Theorems · Theorem · category theory

CategoryTheory.Presieve.isSheafFor_pullback_iff

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

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsIso