Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.Covers
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} → CategoryTheory.GrothendieckTopology C → CategoryTheory.Sieve X → (Y ⟶ X) → PropThe sieve S on X J-covers an arrow f to X if S.pullback f ∈ J Y.
This definition is an alternate way of presenting a Grothendieck topology.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 32 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.pullbackproof · cited by 126
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.closeproof · cited by 13
- CategoryTheory.GrothendieckTopology.IsClosedproof · cited by 10
- CategoryTheory.GrothendieckTopology.covers_iffstatement · cited by 4
- CategoryTheory.classifier_isSheafproof · cited by 4
- CategoryTheory.GrothendieckTopology.close_isClosedproof · cited by 3
- CategoryTheory.GrothendieckTopology.mem_iff_isSheafFor_closedSievesproof · cited by 2
- CategoryTheory.GrothendieckTopology.isClosed_pullbackproof · cited by 1
- CategoryTheory.GrothendieckTopology.arrow_intersectstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.arrow_maxstatement · cited by 1
- CategoryTheory.GrothendieckTopology.arrow_transstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.covers_iff_mem_of_isClosedstatement · cited by 1