Theorems · Theorem · category theory
CategoryTheory.Coverage.saturate_of_superset
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (K : CategoryTheory.Coverage C) {X : C}
{S T : CategoryTheory.Sieve X}, S ≤ T → K.Saturate X S → K.Saturate X T- Defined in
- Mathlib.CategoryTheory.Sites.Coverage
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsproof · cited by 446
- CategoryTheory.Coveragestatement and proof · cited by 31
- CategoryTheory.Coverage.Saturatestatement and proof · cited by 14
- CategoryTheory.Coverage.eq_top_pullbackproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Coverage.mem_toGrothendieck_sieves_of_supersetproof · cited by 2
- CategoryTheory.extensive_regular_generate_coherentproof · cited by 2
- CategoryTheory.Pretopology.toGrothendieck_toCoverageproof · cited by 1
- CategoryTheory.regularTopology.mem_sieves_of_hasEffectiveEpiproof · cited by 1
- CategoryTheory.Coverage.Saturate.pullbackproof · cited by 0