Using of category theory in computer science has extremely grown in the last decade. Categories allow us to express mathematical structures in unified way. Algebras are used for constructing basic structures used in computer programs. A program can be considered as an element of the initial algebra arising from the used programming language. In our contribution we formulate two ways of expressi...

For a finite dimensional algebra A over an algebraically closed field, let T (A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if TA is a tilting module and B = EndTA, then T (A) is tame if and only if T (B) is tame. Introduction. Let k be an algebraically closed field. In this paper, an algebra A is always assumed to be associative, with an ide...

The completeness theorem of equational logic of Birkhoff asserts the coincidence of the model-theoretic and proof-theoretic consequence relations. Goguen and Meseguer, giving a sound and adequate system of inference rules for many-sorted deduction, founded ultimately on the congruences on Hall algebras, generalized the completeness theorem of Birkhoff to the completeness theorem of many-sorted ...

We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. That is, the category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.

Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes finite algebras closed under products, subalgebras and quotients. In this article, is generalized to Eilenberg-Moore a monad T on category D: we prove class -algebras pseudovariety iff it presentable by profinit...

Let SMC denote the 2-category with objects small symmetric monoidal categories, 1cells symmetric monoidal functors and 2-cells monoidal natural transformations. It is shown that the category quotient of SMC by the congruence generated by its 2-cells is symmetric monoidal closed. 1 Summary of results Thomason’s famous result claims that symmetric monoidal categories model all connective spectra ...

We introduce modal de Vries algebras and develop a duality between the category of modal de Vries algebras and the category of coalgebras for the Vietoris functor on compact Hausdorff spaces. This duality serves as a common generalization of de Vries duality between de Vries algebras and compact Hausdorff spaces, and the duality between modal algebras and modal spaces.

A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in [Li6]. In this current paper, we develop this theory of quasi modules at infinity for vertex algebras further. Among the main results, we obtain a commutator formula for general quasi modules at infinity and we establish a category equivalence between the category of qu...