Theorems · Definition · category theory
Preorder.semilatticeInfOfHasBinaryProducts
(C : Type u) → [inst : PartialOrder C] → [CategoryTheory.Limits.HasBinaryProducts C] → SemilatticeInf C
If a partial order has binary products, then it is an inf-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
- SemilatticeInfstatement · cited by 634
- CategoryTheory.Limits.prod.fstproof · cited by 189
- CategoryTheory.Limits.prod.sndproof · cited by 185
- CategoryTheory.Limits.BinaryFan.mkproof · cited by 112
- CategoryTheory.Limits.HasBinaryProductsstatement and proof · cited by 79
- CategoryTheory.Limits.prodIsProdproof · cited by 7
- Preorder.semilatticeInfOfIsLimitBinaryFanproof · cited by 0
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