ComK may be defined as the (cartesian closed) category of comonoids in chuK , or equivalently as dictionaries D for which any crossword over D has its main diagonal in D. Com2 resembles Top, ordinary topological spaces. Common to both are the Alexandroff posets and the Scott DCPOs, while the topological space R and the dual DCPO {−∞ < . . . < −2 < −1 < 0} jointly witness the incomparability of ...

Various situations in computer science call for categories that support both cartesian closed and monoidal closed structure. Such situations include (i) models of local state, where the monoidal product describes disjointness of memory, and (ii) treatment of fresh names, as required in models of the π-calculus. I propose a technique to embed the two closed structures into one single structure. ...

A setoid is a set together with a constructive representation of an equivalencerelation on it. Here, we give category theoretic support to the notion. Wefirst define a category Setoid and prove it is cartesian closed with coproducts.We then enrich it in the cartesian closed category Equiv of sets and classicalequivalence relations, extend the above results, and prove that Setoid...

One natural way to generalize Domain Theory is to replace partially ordered sets by categories. This kind of generalization has recently found application in the study of concurrency. An outline is given of the elegant mathematical foundations which have been developed. This is specialized to give a construction of cartesian closed categories of domains, which throws light on standard presentat...

Frölicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C∞(M, G) or Diff(M), but also projective limits of Lie groups are in a natural way objects of that category, and group operations are morphisms in the category. We call groups with this property Frölicher groups. One can define tangent spaces...

We obtain a characterization of the completion of an initial uniform convergence structure, which includes, among others, subspaces and projective limits of uniform convergence spaces. In this regard, there seems to be a gap in the literature. This characterization is obtained in a surprisingly straightforward way, and this should be viewed as a consequence of the fact that the category UCS of ...

The paper considers algebraic directed-complete partial orders with a semi-regular Scott topology, called regular domains. As is well known, the category of Scott domains and continuous maps is Cartesian closed. This is no longer true, if the domains are required to be regular. Two Cartesian closed subcategories of the regular Scott domains are exhibited: regular dI-domains with stable maps and...

We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed -calculus and cartesian closed categories, we define a new typed framework, called dou...