We build a cartesian closed category, called Cho, based on event structures. It allows an interpretation of higher-order stateful concurrent programs that is refined and precise: on the one hand it is conservative with respect to standard Hyland-Ong games when interpreting purely functional programs as innocent strategies, while on the other hand it is much more expressive. The interpretation o...

We give a categorical semantics to the call-by-name and call-by-value versions of Parigot’s -calculus with disjunction types. We introduce the class of control categories, which combine a cartesian-closed structure with a premonoidal structure in the sense of Power and Robinson. We prove, via a categorical structure theorem, that the categorical semantics is equivalent to a CPS semantics in the...

In the first part of this note an elementary proof is given of the fact that algebraic functors, that is, functors induced by morphisms of Lawvere theories, have left adjoints provided that the category K in which the models of these theories take their values is locally presentable. The main focus however lies on the special cases of the underlying functor of the category Grp(K) of internal gr...

We propose a typed calculus of synchronous processes based on the structure of interaction categories. Our aim has been to develop a calculus for concurrency that is canonical in the sense that the typed-calculus is canonical for functional computation. We show strong connections between syntax, logic and semantics, analogous to the familiar correspondence between the typed-calculus, intuitioni...

We call a nitely complete category algebraically coherent if the change-ofbase functors of its bration of points are coherent, which means that they preserve nite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdor algebras over a ...

In this paper I compare two well studied approaches to topological semantics| the domain-theoretic approach, exempli ed by the category of countably based equilogical spaces, Equ, and Type Two E ectivity, exempli ed by the category of Baire space representations, Rep(B ). These two categories are both locally cartesian closed extensions of countably based T0-spaces. A natural question to ask is...

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truthvalue in standard logic are subsumed by the notions of process and flow in dialectical logic. Dialectical logic has a standard aspect, which can be defined in terms of the “local cartesian closu...

We introduce container functors as a representation of data types providing a new conceptual analysis of data structures and polymorphic functions. Our development exploits Type Theory as a convenient way to define constructions within locally cartesian closed categories. We show that container morphisms can be full and faithfully interpreted as polymorphic functions (i.e. natural transformatio...

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

We introduce the notion of quasi-zero-dimensionality as a substitute for the notion of zero-dimensionality, motivated by the fact that the latter behaves badly in the realm of qcb-spaces. We prove that the category QZ of quasi-zero-dimensional qcb0-spaces is cartesian closed. Prominent examples of spaces in QZ are the spaces of the Kleene-Kreisel continuous functionals equipped with the respect...