Weighted colimits and formal balls in generalized metric spaces

(a) Limits of Cauchy sequences in a (possibly non-symmetric) metric space are shown to be weighted colimits (a notion introduced by Borceux and Kelly, 1975). As a consequence, further insights from enriched category theory are applicable to the theory of metric spaces, thus continuing Lawvere's (1973) approach. Many of the recently proposed d

Weighted colimits and formal balls in generalized metric spaces

(a) Limits of Cauchy sequences in a (possibly non-symmetric) metric space are shown to be weighted colimits (a notion introduced by Borceux and Kelly, 1975). As a consequence, further insights from enriched category theory are applicable to the theory of metric spaces, thus continuing Lawvere's (1973) approach. Many of the recently proposed d

Coinductive counting : bisimulation in enumerative combinatorics

The recently developed coinductive calculus of streams finds here a further application in enumerative combinatorics. A general methodology is developed to solve a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite (weighted) automaton; (2) the automaton is minimized b

Coalgebra, concurrency and control

Coalgebra is used to generalize notions and techniques from concurrency theory, in order to apply them to problems concerning the supervisory control of discrete event systems. The main ingredients of this approach are the characterization of controllability in terms of (a variant of) the notion of bisimulation, and the observation that the fa

Elements of generalized ultrametric domain theory

Generalized ultrametric spaces are a common generalization of preorders and ordinary ultra-metric spaces, as was observed by Lawvere (1973). Guided by his enriched-categorical view on (ultra)metric spaces, we generalize the standard notions of Cau