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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupproof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- CategoryTheory.Limits.Coconestatement · cited by 746
- CategoryTheory.Pairwisestatement · cited by 40
- CategoryTheory.Pairwise.diagramstatement · cited by 30
- CategoryTheory.Pairwise.coconeιAppproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.IsSheafPairwiseIntersectionsproof · cited by 3
- TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_typesproof · cited by 2
- TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersectionsstatement · cited by 2
- CategoryTheory.Pairwise.coconeIsColimitstatement · cited by 2
- TopCat.Presheaf.isLimitOpensLeCoverEquivPairwisestatement · cited by 2
- TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_typesproof · cited by 1
- TopCat.Presheaf.SheafConditionPairwiseIntersections.isLimitMapConeOfIsLimitSheafConditionForkstatement and proof · cited by 1
- TopCat.Presheaf.SheafConditionPairwiseIntersections.isLimitSheafConditionForkOfIsLimitMapConestatement and proof · cited by 1
- TopCat.Sheaf.interUnionPullbackConeLift_leftproof · cited by 0
- TopCat.Sheaf.interUnionPullbackConeLift_rightproof · cited by 0
- CategoryTheory.Pairwise.cocone_ptstatement and proof · cited by 0
- CategoryTheory.Pairwise.cocone_ι_appstatement and proof · cited by 0