Theorems · Definition · category theory
Preorder.semilatticeSupOfHasBinaryCoproducts
(C : Type u) → [inst : PartialOrder C] → [CategoryTheory.Limits.HasBinaryCoproducts C] → SemilatticeSup C
If a partial order has binary coproducts, then it is a sup-semilattice
- Defined in
- Mathlib.CategoryTheory.Limits.Preorder
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- SemilatticeSupstatement · cited by 785
- CategoryTheory.Limits.coprod.inlproof · cited by 137
- CategoryTheory.Limits.coprod.inrproof · cited by 132
- CategoryTheory.Limits.HasBinaryCoproductsstatement and proof · cited by 98
- CategoryTheory.Limits.BinaryCofan.mkproof · cited by 83
- CategoryTheory.Limits.coprodIsCoprodproof · cited by 11
- Preorder.semilatticeSupOfIsColimitBinaryCofanproof · cited by 0
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