Along the lines of classical categorical type theory for total functions, we establish correspondence results between certain classes of partial equational theories on the one hand and suitable classes of categories having certain finite limits on the other hand. E.g., we show that finitary partial theories with existentially conditioned equations are essentially the same as cartesian categorie...

In [8] and [9] Moisil has introduced the resemblance relations. Following [9] we associate to every resemblance relation an extensive operator which commutes with arbitrary unions of sets. We are leading to consider spaces endowed with such closure operators; we shall call these spaces total tech spaces (TC-spaces). TC-spaces are in one-to-one, onto correspondence with reflexive relations. TC-s...

We define a faithful functor from a cartesian closed category of linearly topologized vector spaces over a field and generalized polynomial functions to the category of “extensional” presheaves over the Lawvere theory of polynomial functions, and show that, under some conditions on the field, this functor is full and preserves the cartesian closed structure.

We present a cartesian closed category of dI-domains with coherence and strongly stable functions which provides a new model of PCF, where terms are interpreted by functions and where, at rst order, all functions are sequential. We show how this model can be reened in such a way that the theory it induces on the terms of PCF be strictly ner than the theory induced by the Scott model of continuo...

A result by Curien establishes that filiform concrete data structures can be viewed as games. We extend the idea to cover all stable concrete data structures. This necessitates a theory of games with an equivalence relation on positions. We present a faithful functor from the category of concrete data structures to this new category of games, allowing a game-like reading of the former. It is po...

The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species c...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compression of event structures as an example of quotient: the compression of an event structure E is a m...

The long-standing problem of nding the maximal cartesian closed categories of continuous domains is solved. The solution requires the de nition of a new class of continuous domains, called FS-domains, which contains all retracts of SFPobjects. The properties of FS-domains are discussed in some detail.