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...

For a small category K enriched over a suitable monoidal category V , the free completion of K under colimits is the presheaf category [K ,V ]. If K is large, its free completion under colimits is the V -category PK of small presheaves on K , where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed struct...

This paper describes a category theory semantics for conceptual data modeling. The conceptual data modeling technique used can be seen as a generalization of most existing conceptual data modeling techniques. It contains features such as specialization, generalization , and power types. The semantics uses only simple category theory constructs such as (co)limits and epi-and monomorphisms. There...

A ‘Chen space’ is a set X equipped with a collection of ‘plots’ — maps from convex sets to X — satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold, the category of all Chen spaces is much better behaved than the category of smooth manifolds. For example, any subspace or quotient space of a Chen space is a Chen space, and the space of smooth ma...

This article 1 has two parts: In the rst part, we present some general results about xpoint objects. The minimal categorical structure required to model soundly the equational type theory which combines higher order recursion and computation types (introduced by 4]) is shown to be precisely a let-category possessing a xpoint object. Functional completeness for such categories is developed. We a...

Let ~ C be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category ~ C is called ~ C-closed if for each morphism Φ ⊂ X×Y in the category ~ C the image Φ(X) = {y ∈ Y : ∃x ∈ X (x, y) ∈ Φ} is closed in Y. In the paper we survey existing and new results on topological groups, which are ~...

Jacobs, B., Comprehension categories and the semantics of type dependency, Theoretical Computer Science 107 (1993) 169-207. A comprehension category is defined as a functor 8: E-+B’ satisfying (a) cod 0 9 is a fibration, and (b) fis Cartesian in E implies that qfis a pullback in B. This notion captures many structures which are used to describe type dependency (like display-map categories (Tayl...

We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By “simplicial algebra” we mean any category of algebras over a simplicial algebraic theory, which is allowed to be multi-sorted. The results have applications to the construction of localization model category structures.

the aim of the present paper is to define and study (ic)$lm$-fuzzytopological spaces, a generalization of (weakly) induced $lm$-fuzzytopological spaces. we discuss the basic properties of(ic)$lm$-fuzzy topological spaces, and introduce the notions ofinterior (ic)-fication and exterior (ic)-fication of $lm$-fuzzytopologies and prove that {bf iclm-ftop} (the category of(ic)$lm$-fuzzy topological ...

Introduction. This note is concerned with "categories with internal horn and | and we shall use the terminology from the paper [2] by EIL~.NBERG and Kv.Imy. The result proved may be stated briefly as follows : a Y/--monad ("strong monad") on a symmetric monoidal closed category ~ carries two canonical structures as closed functor. I f these agree (in which case we call the monad commutative), t...