All Questions
Tagged with duality order-theory
7 questions
8
votes
1
answer
551
views
Can one characterize maximal antichains in terms of distributive lattices?
This is inspired by the recent question Verification of a maximal antichain
The celebrated duality between finite posets and finite distributive lattices has several nice formulations. One of them ...
CommunityBot
- 1
4
votes
1
answer
218
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Lattice description of matroid duality
Apologies for this very basic question in matroid theory, but I could not find anything about it online after a bit of searching.
There is a well-known bijective correspondence ("cryptomorphism&...
- 82.7k
9
votes
1
answer
306
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Origin and context of adjunctions inducing equivalences between full subcategories
The following is well-known.
Theorem. Let $F\dashv U$ be a pair of adjoint functors
$$F\colon \mathcal C\to \mathcal D, \qquad U\colon \mathcal D\to\mathcal C$$
with unit $(\eta_A\colon A\to U(F(A)))_{...
- 35.5k
4
votes
0
answers
98
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Unique representability of bounded distributive lattices
Priestley Duality assigns to every bounded distributive lattice $L$ a compact totally order-disconnected topological space $P(L)$, also called a Priestley space.
A poset $(P,\leq)$ is called (...
- 48.9k
5
votes
0
answers
64
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Characters on monotone functions
Characters on the semigroup $(C_{+}^{b}(\mathbb{R}^{d}),+)$, i.e. on bounded positive continuous functions with the ususal pointwise addition, are known to be of the form $C_{+}^{b}(\mathbb{R}^{d})\ni ...
- 289
3
votes
1
answer
320
views
Profinite completion of a partial order
In Johnstone's Stone Spaces it is proved that the category of profinite partial orders is (equivalent to) the category of ordered Stone spaces (also called Priestley spaces) and that the obvious ...
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- 1
1
vote
0
answers
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Looking for a uniform explanation of algebras with canonical generators.
Let $\mathcal{V}$ be a finitary variety i.e. the algebras for a signature whose operations have finite arity and for some arbitrary set of equations. Then any algebra $A \in \mathcal{V}$ has a ...
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