A locally small category E is totally distributive (as defined by Rosebrugh-Wood) if there exists a string of adjoint functors t ⊣ c ⊣ y, where y : E → Ê is the Yoneda embedding. Saying that E is lex totally distributive if, moreover, the left adjoint t preserves finite limits, we show that the lex totally distributive categories with a small set of generators are exactly the injective Grothend...

We describe receptive and distributive needle/syringe sharing among injection drug users (IDUs) in Kabul, Afghanistan. In this cross-sectional study, IDUs completed an interviewer-administered questionnaire. Logistic regression identified correlates of needle sharing in the last six months. Receptive and distributive sharing in the last six months were reported by 28.2% and 28.7% of participant...

Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This generalizes the well-known given by Birkhoff lattices posets. We also study concepts of dual atoms, boolean elements, complemented elements and irreducible elements. prove that sets form semi-boolean algebras. show set lattice lattice.

Let X be an infinite set of cardinality κ. We show that if L is an algebraic and dually algebraic distributive lattice with at most 2 completely join irreducibles, then there exists a monoidal interval in the clone lattice on X which is isomorphic to the lattice 1 + L obtained by adding a new smallest element to L. In particular, we find that if L is any chain which is an algebraic lattice, and...

For distributive double p-algebras, a close connection is established between being congruence coherent and congruence regular. Every congruence regular distributive double p-algebra is congruence coherent. Even though every congruence coherent distributive double p-algebra that has either a non-empty core or finite range is congruence regular, an example is given that is congruence coherent bu...

We present an overview of the theory of self-distributive quasigroups, both in the two-sided and one-sided cases, and relate the older results to the modern theory of quandles, to which self-distributive quasigroups are a special case. Most attention is paid to the representation results (loop isotopy, linear representation, homogeneous representation), as the main tool to investigate self-dist...

Let K and L be lattices, and let φ be a homomorphism of K into L. Then φ induces a natural 0-preserving join-homomorphism of ConK into ConL. Extending a result of A. Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectiv...

This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract , syntax-free contraction-weakening proofs; (3) distribution ; (4) axioms p ∨ p. Abstract propositions correspond to objects of the category G(Rel L) where G is the Hyland-Tan double glue-ing construction, Rel is the standar...