Mathematics – Category Theory
Scientific paper
2005-01-27
Mathematics
Category Theory
29 pages; contains a more elaborate introduction, corrects some typos, and has a sexier title than the previously posted versi
Scientific paper
It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize themselves quite naturally in a quantale, or more generally, a quantaloid. In fact, we are lead to consider cocomplete quantaloid-enriched categories as fundamental mathematical structure for a dynamic logic common to both computer science and physics. Here we explain the theory of totally continuous cocomplete categories as generalization of the well-known theory of totally continuous suplattices. That is to say, we undertake some first steps towards a theory of "dynamic domains''.
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