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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.diagram

Given 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.

CategoryTheory.Presheaf.isSheaf_iff_isLimit · cited by 6Presheaf.isSheaf_iff_isLi…CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit · cited by 4Sieve.forallYonedaIsSheaf…CategoryTheory.GrothendieckTopology.Point.isSheaf_skyscraperPresheaf · cited by 2Point.isSheaf_skyscraperP…CategoryTheory.Presheaf.isLimit_iff_isSheafFor · cited by 2Presheaf.isLimit_iff_isSh…CategoryTheory.PresheafHom.IsSheafFor.app · cited by 2IsSheafFor.appTopCat.Presheaf.whiskerIsoMapGenerateCocone · cited by 2Presheaf.whiskerIsoMapGen…TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover · cited by 2Presheaf.isSheaf_iff_isSh…CategoryTheory.isColimitOfEffectiveEpiFamilyStruct · cited by 2CategoryTheory.isColimitO…CategoryTheory.isColimitOfEffectiveEpiStruct · cited by 2CategoryTheory.isColimitO…CategoryTheory.Presheaf.isSheaf_of_isSheaf_comp · cited by 2Presheaf.isSheaf_of_isShe…CategoryTheory.Presheaf.homEquivAmalgamation · cited by 2Presheaf.homEquivAmalgama…CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve · cited by 1Presheaf.isLimit_iff_isSh…CategoryTheory.effectiveEpiFamilyStructOfIsColimit · cited by 1CategoryTheory.effectiveE…CategoryTheory.effectiveEpiStructOfIsColimit · cited by 1CategoryTheory.effectiveE…CategoryTheory.PresheafHom.IsSheafFor.app_cond · cited by 1IsSheafFor.app_condCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Limits.Cocone · cited by 746Limits.CoconeCategoryTheory.Over.left · cited by 541Over.leftCategoryTheory.Presieve · cited by 449CategoryTheory.PresieveCategoryTheory.Over.hom · cited by 370Over.homCategoryTheory.ObjectProperty.ι · cited by 95ObjectProperty.ιCategoryTheory.Limits.Cocone.whisker · cited by 40Cocone.whiskerCategoryTheory.Presieve.category · cited by 38Presieve.categoryCategoryTheory.Presieve.diagram · cited by 17Presieve.diagramCategoryTheory.Over.forgetCocone · cited by 2Over.forgetCoconePresieve.coconeCITED BYCITES

Cites11

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Cited by34

Results whose statement or proof uses this declaration.