Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.Cover.shape
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X : C} → {J : CategoryTheory.GrothendieckTopology C} → J.Cover X → CategoryTheory.Limits.MulticospanShapeThe shape of the multiequalizer diagrams associated to S : J.Cover X.
- Cited by
- 147 results in Mathlib
- Foundations
- Depth 35 from the axioms, rests on 233 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.GrothendieckTopology.Coverstatement and proof · cited by 211
- CategoryTheory.Limits.MulticospanShapestatement · cited by 160
- CategoryTheory.GrothendieckTopology.Cover.Arrowproof · cited by 99
- CategoryTheory.GrothendieckTopology.Cover.Relationproof · cited by 25
- CategoryTheory.GrothendieckTopology.Cover.Relation.fstproof · cited by 22
- CategoryTheory.GrothendieckTopology.Cover.Relation.sndproof · cited by 22
Cited by217
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.Cover.indexstatement and proof · cited by 142
- CategoryTheory.GrothendieckTopology.plusObjstatement · cited by 56
- CategoryTheory.GrothendieckTopology.sheafifystatement · cited by 32
- CategoryTheory.GrothendieckTopology.diagramstatement and proof · cited by 29
- CategoryTheory.GrothendieckTopology.toPlusstatement · cited by 28
- CategoryTheory.GrothendieckTopology.plusMapstatement · cited by 26
- CategoryTheory.GrothendieckTopology.plusCompIsostatement · cited by 20
- CategoryTheory.GrothendieckTopology.toSheafifystatement · cited by 19
- CategoryTheory.GrothendieckTopology.diagramNatTransstatement and proof · cited by 12
- CategoryTheory.GrothendieckTopology.sheafifyCompIsostatement · cited by 11
- CategoryTheory.GrothendieckTopology.plusLiftstatement · cited by 10
- CategoryTheory.GrothendieckTopology.sheafifyLiftstatement · cited by 9
Showing the 200 most cited of 217.