Theorems · Definition · category theory
CategoryTheory.Precoverage.coverings
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
CategoryTheory.Precoverage C → (X : C) → Set (CategoryTheory.Presieve X)The collection of covering presieves for an object X.
- Defined in
- Mathlib.CategoryTheory.Sites.Precoverage
- Cited by
- 194 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 10 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Presievestatement · cited by 449
- CategoryTheory.Precoveragestatement and proof · cited by 204
Cited by259
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.comapproof · cited by 27
- CategoryTheory.Precoverage.ZeroHypercover.mem₀statement · cited by 26
- CategoryTheory.Pretopology.toGrothendieckproof · cited by 18
- CategoryTheory.Precoverage.generate_mem_toGrothendieckstatement and proof · cited by 12
- CategoryTheory.Precoverage.morphismPropertyproof · cited by 9
- CategoryTheory.Presieve.isSheaf_coveragestatement and proof · cited by 8
- CategoryTheory.Precoverage.mem_iff_exists_zeroHypercoverstatement and proof · cited by 8
- CategoryTheory.Precoverage.toCoverageproof · cited by 7
- CategoryTheory.Precoverage.toPretopologyproof · cited by 6
- CategoryTheory.Precoverage.extstatement and proof · cited by 5
- CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpiproof · cited by 4
- CategoryTheory.PreZeroHypercover.presieve₀_mem_precoverage_iffstatement and proof · cited by 4
Showing the 200 most cited of 259.