  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''.
