Theorems · Theorem · category theory

CategoryTheory.Presieve.restrict_extend

∀ {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},
  x.Compatible → CategoryTheory.Presieve.FamilyOfElements.restrict ⋯ x.sieveExtend = x

The restriction of an extension is the original.

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

3 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category