×

A bicategorical approach to information flow and security. (English) Zbl 0973.90014

Betti, Renato (ed.) et al., Categorical studies in Italy. Selected papers presented at the meeting “The Italian friends meet Bill Lawvere”, Perugia, Italy, May 1-3, 1997. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 64, 99-122 (2000).
Summary: We generalize Sutherland’s notion of information flow and security, treating systems as the objects and interfaces as the morphisms of a bicategory, which may be that of sets and relations, or that of ordered sets and ideals, or something more general. Representing two users of a system \(S\) by maps \(f:S\to A\) and \(g:S\to B\), where a map \(f\) is a morphism with a right adjoint \(f^*\), we use the morphism \(gf^*\) as a measure of information flow, and study the functorial properties of the process sending \((f,g)\) to \(gf^*\), and the existence in many cases of a right adjoint to it.
For the entire collection see [Zbl 0942.00025].

MSC:

90B10 Deterministic network models in operations research
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
90B15 Stochastic network models in operations research
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
PDFBibTeX XMLCite