Unique factorisation lifting functors and categories of linearly-controlled processes

Authors:
Marta Bunge;Marcelo P. Fiore
Affiliations:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6;Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Venue:
Mathematical Structures in Computer Science
Year:
2000

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Abstract

We consider processes consisting of a category of states varying over a control category as prescribed by a unique factorisation lifting functor. After a brief analysis of the structure of general processes in this setting, we restrict attention to linearly-controlled ones. To this end, we introduce and study a notion of path-linearisable category in which any two paths of morphisms with equal composites can be linearised (or interleaved) in a canonical fashion. Our main result is that categories of linearly-controlled processes (viz., processes controlled by path-linearisable categories) are sheaf models.