Theorems · Theorem · category theory

CategoryTheory.Presieve.pullbackCompatible_iff

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
  {R : CategoryTheory.Presieve X} (x : CategoryTheory.Presieve.FamilyOfElements P R) [inst_1 : R.HasPairwisePullbacks],
  x.Compatible ↔ x.PullbackCompatible

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

1 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Presieve.HasPairwisePullbacks