Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.le_close_of_isClosed

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J₁ : CategoryTheory.GrothendieckTopology C) {X : C}
  {S T : CategoryTheory.Sieve X}, S ≤ T → J₁.IsClosed T → J₁.close S ≤ T

The closure of a sieve S is the largest closed sieve which contains S (justifying the name "closure").

Defined in

Mathlib.CategoryTheory.Sites.Closed

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category