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...

Let D1, D2, D be non empty sets and let x be an element of [: [:D1, D2 :], D :]. Then x1,1 is an element of D1. Then x1,2 is an element of D2. Let D1, D2 be non empty sets and let x be an element of [:D1, D2 :]. Then x2 is an element of D2. Next we state the proposition (1) Let C, D be category structures. Suppose the category structure of C = the category structure of D. If C is category-like,...

One approach to the study of wear involves the ch~~te~zation of surface failure under conditions of single-pass sliding. Such an approach has been used to show that the wear of commercial and experimental restorative resins and composites is determined by the resistance of the material to penetration and by the mode of deformation during sliding [l] . The purpose of this investigation was to ch...

In computational linguistics, a large body of work exists on distributed modeling lexical relations, focussing largely relations such as hypernymy (scientist -- person) that hold between two categories, expressed by common nouns. contrast, linguistics has paid little attention to entities denoted proper nouns (Marie Curie, Mumbai, ...). These have investigated in detail the Knowledge Representa...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

Estimates of the IT workforce depend, first, on the definition of “IT worker” used. For example, estimating the number of Category 1 IT workers would yield a very different result (Table B.1) than would estimating the combined total of Category 1 and Category 2 workers (Table B.2). Similarly, estimating the number of individuals in software occupations would be a different exercise from estimat...

Dangerous pathogens are defined by the UK Health and Safety Executive's advisory committee as category 3 (those which cause severe human disease for which prophylaxis or therapy is usually available) or category 4 (as for category 3, but for which prophylaxis or therapy is not available). Research and development of vaccines for such pathogens is challenging, due to the safety constraints in th...

The λ-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 λ-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 mod...