A category theoretical background for homomorphism theorems
A characterization of quasivarieties of partial algebras by means of limits and products.
A duality for isotropic median algebras
We establish categorical dualities between varieties of isotropic median algebras and suitable categories of operational and relational topological structures. We follow a general duality theory of B.A. Davey and H. Werner. The duality results are used to describe free isotropic median algebras. If the number of free generators is less than five, the description is detailed.
A groupoid characterization of Boolean algebras
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
A new proof of Reiterman's theorem
A note on isomorphic varieties
A note on reflective subcategories defined by partial algebras
A property of stable theories
A remark on topological spaces, grids, and topological systems
A sufficient condition for a variety to have the amalgamation property
A unified syntactical approach to theorems of Putcha, Margolis, and Straubing on finite power semigroups.
Absolutely closed spaces and categories of algebras
Adjointness between theories and strict theories
The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols. If the object class of a dhts-category...
Aggregation operators on partially ordered sets and their categorical foundations
In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of -fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators...
Algebraic duality of constant algebras
Algebraic properties of Husimi trees
Algebraic theories and varieties of functor algebras
Algebras over theories
Almost ff-universal and q-universal varieties of modular 0-lattices
A variety 𝕍 of algebras of a finite type is almost ff-universal if there is a finiteness-preserving faithful functor F: 𝔾 → 𝕍 from the category 𝔾 of all graphs and their compatible maps such that Fγ is nonconstant for every γ and every nonconstant homomorphism h: FG → FG' has the form h = Fγ for some γ: G → G'. A variety 𝕍 is Q-universal if its lattice of subquasivarieties has the lattice of subquasivarieties of any quasivariety of algebras of a finite type as the quotient of its sublattice....
An Elementary Characterization of the Category of (Free) Relational Systems.