We study categories of partial algebras of the same type In these categories we de ne a binary operation of exponentiation for objects and investigate its behaviour We discover two cartesian closed initially structured subcategories in every category of partial algebras of the same type It is well known that concrete categories having well behaved func tion spaces i e being initially structured...

Infinite dimensional spaces frequently appear in physics; there are several approaches to obtain a good categorical framework for this type of space, and cartesian closedness of some category, embedding smooth manifolds, is one of the most requested condition. In the first part of the paper, we start from the failures presented by the classical Banach manifolds approach and we will review the m...

L-sets over a base set X are generalizations of classical sets where subsets are not specified by characteristic functions from X to {0, 1} but rather by functions from X to a lattice L. For an L-set a ∈ L and an element x ∈ X, a(x) is interpreted as the grade of membership of x in a. Stratified L-topological spaces are generalizations of topological spaces to the L-set case [1]. In [2], strati...

Keywords: Exponential subcategory of a category, cartesian closed category, initially structured category, category of partial algebras of the same type, partial algebra fulllling the interchange law, diagonal partial algebra. Abstract: We study categories of partial algebras of the same type. In these categories we deene a binary operation of exponentiation for objects and investigate its beha...

The-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from category theory, the usual calculus of-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a \minimal" topological model, ...

We can regard operations that discard information, like specializing to a particular case or dropping the intermediate steps of a proof, as projections, and operations that reconstruct information as liftings. By working with several projections in parallel we can make sense of statements like “Set is the archetypal Cartesian Closed Category”, which means that proofs about CCCs can be done in t...

We generalize the standard construction of realizability models (specifically, of categories of assemblies) to a wide class of computability structures, broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion of simulation between such computability structures, and show how these simulations correspond precisely to cer...

1 is unique (1 = 11 = 1, so any left identity equals any right identity). A morphism takes 1 to the identity of φX (since φ(x) = φ(1x) = φ(1)φ(x)), but φ(1) = 1 is an extra property that ought to be satisfied by morphisms; its kernel is the sub-algebra φ(1); zero object is { 1 }; not Cartesian-closed (the terminal and initial objects are the same, yet not all groups are isomorphic). A quasi-gro...

Synopsis. In a cartesian closed category with an initial object and a dominance that classiies it, an intensional notion of approximation between maps |the path relation (c.f. link relation)| is deened. It is shown that if such a category admits strict/upper-closed factorisations then it preorder-enriches (as a cartesian closed category) with respect to the path relation. By imposing further ax...