THE CATEGORY THEORY OF TIME SYSTEMS |
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Authors: | YASUHIKO TAKAHARA TETSUO TAKAI |
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Affiliation: | Department of System Science , Tokyo Institute of Technology , 4259 Nagatsuta, Midori-ku, Yokohama, 227, Japan |
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Abstract: | In this paper we show a categorical treatment of general time systems using the categorization method presented in our previous paper. Various concepts about general time systems are categorized in the unified framework. Some category theoretical tools for the investigation of such time systems are presented. Using those tools some basic properties of time systems are explored in our framework. In particular, a conceptual equivalence between the causality and the state space representability is proved in the categorical terms. These results show that our method can be a universal tool for a categorization and a categorical treatment of mathematically defined general systems. |
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Keywords: | Category of C-time systems sampling functor sampling system inverse limit past determined non-anticipatory canonical representability C-time system C-initial representation modeling morphism |
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