This is the first extensive treatment of the theory of corings and their comodules. In the first
part, the module-theoretic aspects of coalgebras over commutative rings are described …

We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of
topological theories in dimension two, using it to produce interesting theories that do not …

We study the existence of universal measuring comonoids P (A, B) for a pair of monoids A, B
in a braided monoidal closed category, and the associated enrichment of the category of …

As left adjoint to the dual algebra functor, Sweedler's finite dual construction is an important
tool in the theory of Hopf algebras over a field. We show in this note that the left adjoint to the …

The main aim of this paper is to give a Hopf algebroid approach to the Picard-Vessiot theory
of linear differential matrix equations with coefficients in the polynomial complex algebra. To …

Let A be an algebra over a commutative ring R. If R is noetherian and A° is pure in RA, then
the categories of rational left A-modules and right A°-comodules are isomorphic. In the Hopf …

We extend the theory of Sweeder's measuring comonoids to the framework of duoidal
categories: categories equipped with two compatible monoidal structures. We use one of the …

Prime objects were defined as generalization of simple objects in the categories of rings
(modules). In this paper we introduce and investigate what turns out to be a suitable …

The grouplike elements of a coalgebra over a field are known to be linearly independent
over said field. Here we prove three variants of this result. One is a generalization to …

In this paper we improve and extend duality theorems for crossed products obtained by M.
Koppinen (C. Chen) from the case of base fields (Dedekind domains) to the case of arbitrary …