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Enriched categories and models for spaces of evolving states. (English) Zbl 1148.18004

Summary: Partially ordered sets, causets, partially ordered spaces, and their local counterparts are now often used to model systems in computer science and theoretical physics. The order models ‘time’ which is often not globally given. In this setting, directed paths are important objects of study, as they correspond to an evolving state or particle traversing the system. We model both the ‘space’ and the directed paths by a simplicially enriched category, and show how to adapt some classical constructions to produce a differential graded enrichment.

MSC:

18D20 Enriched categories (over closed or monoidal categories)
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
55U10 Simplicial sets and complexes in algebraic topology
18B20 Categories of machines, automata
18G55 Nonabelian homotopical algebra (MSC2010)
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
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