Restriction categories as enriched categories

Restriction categories as enriched categories

Article history: Received 27 November 2012 Received in revised form 4 September 2013 Accepted 20 December 2013 Communicated by B.P.F. Jacobs

Convergence and quantale-enriched categories

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

Enriched Categories as Models of Computation

In this paper we discuss a general methodology to provide a categorical semantics for a wide class of computational systems, whose behaviour can be described by a suitable set of transition steps. We open our survey presenting some results on the semantics of Petri Nets. Starting from this, we elaborate a two-steps procedure allowing for the description of all the sequences of transitions perfo...

Probabilistic metric spaces as enriched categories

Restriction categories I: categories of partial maps

Given a category with a stable system of monics, one can form the corresponding category of partial maps. To each map in this category there is, on the domain of the map, an associated idempotent, which measures the degree of partiality. This structure is captured abstractly by the notion of a restriction category, in which every arrow is required to have such an associated idempotent. Categori...