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On Piecewise-Linear Homeomorphisms Between Distributive and Anti-blocking Polyhedra
Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear...
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Lattices 1 + L as \(\operatorname {L}_{\text{q}}(\mathcal K)\)
In this chapter we consider conditions under which, given a finite join semidistributive lattice, the linear sum...
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Real Spectrum Versus ℓ-Spectrum via Brumfiel Spectrum
It is well known that the real spectrum of any commutative unital ring, and the ℓ -spectrum of any Abelian lattice-ordered group with order-unit, are...
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Correspondence Theory on Vector Spaces
This paper extends correspondence theory to the framework of \(\mathbb {K}\)...
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Meet meets join: the interaction between pooled and common knowledge
This paper explores the lattice-theoretic properties of the family of all partitions of an arbitrary state space. I discuss a duality correspondence...
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Brown’s Representation Theorem
In this chapter, we observe that every fuzzy lattice is isomorphic to a simple texture and vice versa. Let U be a domain of discourse. The family of...
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Tensor triangular geometry of filtered objects and sheaves
We compute the Balmer spectra of compact objects of tensor triangulated categories whose objects are filtered or graded objects of (or sheaves valued...
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The Canonical Complex of the Weak Order
We define and study the canonical complex of a finite semidistributive lattice L . It is the simplicial complex on the join or meet irreducible...
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Algebraic Presentation of Semifree Monads
Monads and their composition via distributive laws have many applications in program semantics and functional programming. For many interesting...
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\({\mathcal {C}}_1\)-diagrams of slim rectangular semimodular lattices permit quotient diagrams
Slim semimodular lattices (for short, SPS lattices ) and slim rectangular lattices (for short, SR lattices ) were introduced by Grätzer and Knapp (Acta...
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The fundamental theorem of finite semidistributive lattices
We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff’s Fundamental Theorem of Finite Distributive...
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Correspondence Theory for Modal Fairtlough–Mendler Semantics of Intuitionistic Modal Logic
We study the correspondence theory of intuitionistic modal logic in modal Fairtlough–Mendler semantics (modal FM semantics) (Fairtlough and Mendler...
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Generalized absolute values, ideals and homomorphisms in mixed lattice groups
A mixed lattice group is a generalization of a lattice ordered group. The theory of mixed lattice semigroups dates back to the 1970s, but the...
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Introduction
This monograph studies the lattice of subquasivarieties of a quasivariety. We consider both the properties that these lattices have, and which...
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Preclops on Finite Lattices
A preclop is a closure operator on a lattice that satisfies some of the known properties of the equational closure operator on subquasivariety...
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Some further results on pointfree convex geometry
Inspired by locale theory, pointfree convex geometry was first proposed and studied by Yoshihiro Maruyama. In this paper, we shall continue to his...
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On the relation between the subadditivity cone and the quantum entropy cone
Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations...