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Theorems · Definition · category theory

CategoryTheory.Pairwise.cocone

{ι : Type v} →
  {α : Type u} →
    (U : ι → α) → [inst : CompleteLattice α] → CategoryTheory.Limits.Cocone (CategoryTheory.Pairwise.diagram U)

Given a function U : ι → α for [CompleteLattice α], iSup U provides a cocone over diagram U.

Defined in
Mathlib.CategoryTheory.Category.Pairwise
Cited by
8 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteLattice

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopCat.Presheaf.IsSheafPairwiseIntersections · cited by 3Presheaf.IsSheafPairwiseI…TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_types · cited by 2Presheaf.isSheaf_iff_isSh…TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections · cited by 2IsSheaf.isSheafPairwiseIn…CategoryTheory.Pairwise.coconeIsColimit · cited by 2Pairwise.coconeIsColimitTopCat.Presheaf.isLimitOpensLeCoverEquivPairwise · cited by 2Presheaf.isLimitOpensLeCo…TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types · cited by 1IsSheaf.isSheafUniqueGlui…TopCat.Presheaf.SheafConditionPairwiseIntersections.isLimitMapConeOfIsLimitSheafConditionFork · cited by 1SheafConditionPairwiseInt…TopCat.Presheaf.SheafConditionPairwiseIntersections.isLimitSheafConditionForkOfIsLimitMapCone · cited by 1SheafConditionPairwiseInt…TopCat.Sheaf.interUnionPullbackConeLift_left · cited by 0Sheaf.interUnionPullbackC…TopCat.Sheaf.interUnionPullbackConeLift_right · cited by 0Sheaf.interUnionPullbackC…CategoryTheory.Pairwise.cocone_pt · cited by 0Pairwise.cocone_ptCategoryTheory.Pairwise.cocone_ι_app · cited by 0Pairwise.cocone_ι_appTopCat.Presheaf.isGluing_iff_pairwise · cited by 0Presheaf.isGluing_iff_pai…TopCat.Presheaf.SheafCondition.pairwiseCoconeIso · cited by 0SheafCondition.pairwiseCo…iSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeCategoryTheory.Limits.Cocone · cited by 746Limits.CoconeCategoryTheory.Pairwise · cited by 40CategoryTheory.PairwiseCategoryTheory.Pairwise.diagram · cited by 30Pairwise.diagramCategoryTheory.Pairwise.coconeιApp · cited by 1Pairwise.coconeιAppPairwise.coconeCITED BYCITES

Cites6

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Cited by14

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