Theorems · Definition · category theory
CategoryTheory.Sieve.arrows
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → {X : C} → CategoryTheory.Sieve X → CategoryTheory.Presieve Xthe underlying presieve
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 446 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Presievestatement · cited by 449
Cited by544
Results whose statement or proof uses this declaration.
- Opens.grothendieckTopologyproof · cited by 206
- CategoryTheory.Sieve.pullbackproof · cited by 126
- CategoryTheory.Sieve.functorPushforwardproof · cited by 73
- CategoryTheory.Presieve.IsSheafproof · cited by 66
- CategoryTheory.Sieve.functorPullbackproof · cited by 49
- CategoryTheory.Sieve.extstatement and proof · cited by 43
- CategoryTheory.Precoverage.toGrothendieckproof · cited by 41
- CategoryTheory.Sieve.downward_closedstatement · cited by 39
- CategoryTheory.GrothendieckTopology.superset_coveringproof · cited by 37
- CategoryTheory.isSheaf_iff_isSheaf_of_typeproof · cited by 30
- CategoryTheory.typesGrothendieckTopologyproof · cited by 28
- CategoryTheory.Functor.IsDenseSubsite.mapPreimageproof · cited by 23
Showing the 200 most cited of 544.