Towards "dynamic domains": totally continuous cocomplete Q-categories
摘要
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''.
引用
@article{arxiv.math/0501489,
title = {Towards "dynamic domains": totally continuous cocomplete Q-categories},
author = {Isar Stubbe},
journal= {arXiv preprint arXiv:math/0501489},
year = {2007}
}
备注
29 pages; contains a more elaborate introduction, corrects some typos, and has a sexier title than the previously posted version, but the mathematics are essentially the same