Theorems · Definition · category theory
CategoryTheory.Pairwise.coconeIsColimit
{ι : Type v} →
{α : Type u} →
(U : ι → α) → [inst : CompleteLattice α] → CategoryTheory.Limits.IsColimit (CategoryTheory.Pairwise.cocone U)Given a function U : ι → α for [CompleteLattice α],
iInf U provides a limit cone over diagram U.
- Defined in
- Mathlib.CategoryTheory.Category.Pairwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteLatticestatement and proof · cited by 1,048
- CategoryTheory.Limits.IsColimitstatement · cited by 773
- CategoryTheory.Limits.Coconeproof · cited by 746
- CategoryTheory.homOfLEproof · cited by 554
- CategoryTheory.Pairwisestatement · cited by 40
- CategoryTheory.Pairwise.diagramstatement and proof · cited by 30
- CategoryTheory.Pairwise.coconestatement · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.IsSheaf.isSheafPreservesLimitPairwiseIntersectionsproof · cited by 1
- TopCat.Presheaf.isSheaf_iff_isSheafPreservesLimitPairwiseIntersectionsproof · cited by 0