A categorical genealogy for the congruence distributive property.
A categorical generalization of a theorem of G. Birkhoff on primitive classes of universal algebras
A category theoretical background for homomorphism theorems
A certain Galois connection and weak automorphisms
A characterization of arithmetical varieties by two-element subsets
A characterization of congruence classes of quasigroups
A characterization of distributive lattices by tolerance lattices
A characterization of K-ary algebraic categories.
A characterization of modular lattices
A characterization of polarities whose lattice of polars is Boolean
A characterization of quasivarieties of partial algebras by means of limits and products.
A characterization of Sheffer functions by hyperidentities.
A characterization of strong homomorphisms
A characterization of the group congruences on a semigroup.
A characterization of tolerance-distributive tree semilattices
A characterization of varieties of inverse semigroups.
A classification of rational languages by semilattice-ordered monoids
We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.
A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture
The Erdős-Faber-Lovász conjecture states that if a graph G is the union of n cliques of size n no two of which share more than one vertex, then χ(G) = n. We provide a formulation of this conjecture in terms of maximal partial clones of partial operations on a set.
A common generalization of permutability and 0-permutability
A concept of variety for regular biordered sets.