Theorems · Theorem · category theory

CategoryTheory.Presieve.extend_agrees

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X Y : C}
  {R : CategoryTheory.Presieve X} {x : CategoryTheory.Presieve.FamilyOfElements P R},
  x.Compatible → ∀ {f : Y ⟶ X} (hf : R f), x.sieveExtend f ⋯ = x f hf

The extension of a family agrees with the original family.

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

1 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category