Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.isClosed_iff_close_eq_self

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

The sieve S is closed iff its closure is equal to itself.

Defined in

Mathlib.CategoryTheory.Sites.Closed

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category