Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.superset_covering

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C} {S R : CategoryTheory.Sieve X}
  (J : CategoryTheory.GrothendieckTopology C), S ≤ R → S ∈ J X → R ∈ J X

If S is a subset of R, and S is covering, then R is covering as well. See also discussion after [MM92] Chapter III, Section 2, Definition 1.

Defined in

Mathlib.CategoryTheory.Sites.Grothendieck

Cited by

37 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category