based on a complete heyting algebra l, the relations between lfuzzifyingconvergence spaces and l-fuzzifying topological spaces are studied.it is shown that, as a reflective subcategory, the category of l-fuzzifying topologicalspaces could be embedded in the category of l-fuzzifying convergencespaces and the latter is cartesian closed. also the specialization l-preorderof l-fuzzifying convergenc...

First, we briefly recall the main definitions of the theory of Information Bases and Translations. These mathematical structures are the basis to construct the cartesian closed category InfBas, which is equivalent to the category ScDom of Scott Domains. Then, we will show that all the definitions and the proof of all the properties that one needs in order to show that InfBas is indeed a cartesi...

Exercises 1.2 (a) Composition in RC is well-defined by representatives. (b) A morphism of RC is invertible ⇐⇒ it is a class of strong equivalences ⇐⇒ its counit is an isomorphism. (c) Objects of RC are isomorphic iff they are equivalent categories. (d) RC/T ' Copt(T ) (?). Rigid comparisons embody an important idea from domain theory: approximation. This must have the property that if X ′ appro...

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...

From the analogue of Böhm’s Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here of these results, which were obtained previously by Richard Statman and Alex K. Simpson. Mathema...

The category of flows is not cartesian closed. We construct a closed symmetric monoidal structure which has moreover a satisfactory behavior from the computer scientific viewpoint.

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...

However, the replete construction is of a very general nature and most of its properties are independent of the axioms for Σ and of E being a topos. We consider the replete construction in the more general setting of a cartesian closed B-fibration p: C → B, where B is a category with finite products. This encompasses the case of a cartesian closed category (i.e. p: C → 1) and that of a locally ...