Theorems · Definition · category theory
CategoryTheory.Presieve.cocone
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X : C} → (S : CategoryTheory.Presieve X) → CategoryTheory.Limits.Cocone S.diagramGiven a sieve S on X : C, its associated cocone S.cocone is defined to be
the natural cocone over the diagram defined above with cocone point X.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 31 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.
Cites11
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.Overstatement and proof · cited by 935
- CategoryTheory.Limits.Coconestatement · cited by 746
- CategoryTheory.Over.leftstatement and proof · cited by 541
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Over.homstatement and proof · cited by 370
- CategoryTheory.ObjectProperty.ιproof · cited by 95
- CategoryTheory.Limits.Cocone.whiskerproof · cited by 40
- CategoryTheory.Presieve.categorystatement · cited by 38
- CategoryTheory.Presieve.diagramstatement · cited by 17
- CategoryTheory.Over.forgetCoconeproof · cited by 2
Cited by34
Results whose statement or proof uses this declaration.
- CategoryTheory.Presheaf.isSheaf_iff_isLimitstatement and proof · cited by 6
- CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimitstatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.Point.isSheaf_skyscraperPresheafproof · cited by 2
- CategoryTheory.Presheaf.isLimit_iff_isSheafForstatement and proof · cited by 2
- CategoryTheory.PresheafHom.IsSheafFor.appstatement and proof · cited by 2
- TopCat.Presheaf.whiskerIsoMapGenerateCoconestatement · cited by 2
- TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCoverproof · cited by 2
- CategoryTheory.isColimitOfEffectiveEpiFamilyStructstatement · cited by 2
- CategoryTheory.isColimitOfEffectiveEpiStructstatement · cited by 2
- CategoryTheory.Presheaf.isSheaf_of_isSheaf_compproof · cited by 2
- CategoryTheory.Presheaf.homEquivAmalgamationstatement and proof · cited by 2
- CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presievestatement · cited by 1