This paper is a first step in the study of symmetric cat-groups as the 2-dimensional analogue of abelian groups. We show that a morphism of symmetric cat-groups can be factorized as an essentially surjective functor followed by a full and faithful one, as well as a full and essentially surjective functor followed by a faithful one. Both these factorizations… (More)
In this paper a we give a semantics for SCCS using the constructions of the topos of labelled trees. The semantics accounts for all aspects of the original formulation of SCCS, including unbounded non-determinism. Then, a partial solution to the problem of characterizing bisimulation in terms of a class of morphisms is proposed. We deene a class of… (More)
To Aurelio Carboni on his 60th birthday ABSTRACT. We show, for a monad T, that coalgebra structures on a T-algebra can be described in terms of " braidings " , provided that the monad is equipped with an invertible distributive law satisfying the Yang-Baxter equation.
The theoretical study of the relational model of data is ongoing and highly developed. Yet the vast majority of real databases include incomplete data, and the incomplete data is widely modelled using special values called nulls. As noted many times by Date and others, the inclusion of special values is not compatible with the relational model and… (More)
Working in the context of categorical groups, we show that the semidi-rect product provides a biequivalence between actions and points. From this biequivalence, we deduce a 2-dimensional classification of split extensions of categorical groups, as well as the universal property of the holomorph of a categorical group. We also discuss the link between the… (More)