‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

This paper contributes to a line of research that consists in applying qualitative reasoning techniques to the formalization of the case-based inference, and in particular, to its adaptation phase. The importance of capturing case differences has long been acknowledged in adaptation research, but research is still needed to properly represent and reason upon case differences. Assuming that case...

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the yoneda structure [SW78] it generates are explored. Examples relevant to the globular approach to higher dimensional category theory are discussed. This paper also contains some expository material on the theory of fibrations internal to a finitely complete 2category [Str74b] and provi...

The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra framework for Calabi-Yau supermanifolds and stacks in open and closed string theory. In the framework we investigate supersymmetries and integrability.

Directed Algebraic Topology is a recent field, deeply linked with ordinary and higher dimensional Category Theory. A ‘directed space’, e.g. an ordered topological space, has directed homotopies (which are generally non reversible) and a fundamental category (replacing the fundamental groupoid of the classical case). Finding a simple possibly finite model of the latter is a non-trivial problem, ...

Measure and category (or rather, their recursion theoretical counterparts) have been used in Theoretical Computer Science to make precise the intuitive notion \for most of the recursive sets." We use the notions of eeective measure and category to discuss the relative sizes of inferrible sets, and their complements. We nd that inferrible sets become large rather quickly in the standard hierarch...

We study closure properties with respect to products for hypergroupoids, semihypergroups and hypergroups associated to binary relations. Using some basic category theory tools, from a certain point, the investigation turns into studying closure properties with respect to direct products for some classes of monounary multialgebras.

Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined and examined. Applications to the Batanin approach to higher category theory, Joyal species and operads are provided.