The enriched effect calculus is an extension of Moggi’s computational metalanguage with a selection of primitives from linear logic. In this paper, we present an extended case study within the enriched effect calculus: the linear usage of continuations. We show that established call-by-value and call-by name linearly-used CPS translations are uniformly captured by a single generic translation o...

Given a monad T on a suitable enriched category B equipped with a proper factorization system (E ,M ), we define notions of T-completion, T-closure, and T-density. We show that not only the familiar notions of completion, closure, and density in normed vector spaces, but also the notions of sheafification, closure, and density with respect to a Lawvere-Tierney topology, are instances of the giv...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

The availability of semantically enriched data in repositories of larger content providers offers a means for new ways of multimedia presentation authoring. Existing (semi-)automatic content composition environments explore limited numbers of genres and concentrate on templatebased approaches for composing discourse structures for these genres. We analyze a number of genres based on identifiabl...

Many features of current logic programming languages are not captured by conventional semantics. Their fundamentally non-ground character, and the uniform way in which such languages have been extended to typed domains, subject to constraints, suggest that a categorical treatment of constraint domains, of programming syntax and of semantics may be closer in spirit to what declarative programmin...

Meal replacements are a safe and effective tool for weight loss and weight management and beyond. Recent research and concepts suggest that the category can provide additional metabolic and nutritional benefits not previously recognized. Recent studies indicate that use of protein‐enriched meal replacements helps maintain lean body mass during weight loss, providing additional metabolic benefit...

It is known since 1973 that Lawvere’s notion of (Cauchy-)complete enriched category is meaningful for metric spaces: it captures exactly Cauchy-complete metric spaces. In this paper we introduce the corresponding notion of Lawvere completeness for (T,V)-categories and show that it has an interesting meaning for topological spaces and quasi-uniform spaces: for the former ones means weak sobriety...

In a locally λ-presentable category, with λ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are λ-presentable, are known to be characterized by their closure under products, λ-directed colimits and λ-pure subobjects. Replacing the strict commutativity of diagrams by “commutativity up to ε”, this paper provides an “appro...

We investigate what the correct categorical formulation of Hughes’ Arrows should be. It has long been folklore that Arrows, a functional programming construct, and Freyd categories, a categorical notion due to Power, Robinson and Thielecke, are somehow equivalent. In this paper, we show that the situation is more subtle. By considering Arrows wholly within the base category we derive two altern...

Categories play a fundamental role in human cognition. Defining features (short for DFs) are the key elements to define a category, which enables machines to categorize objects. Categories enriched with their DFs significantly improve the machine’s ability of categorization and benefit many applications built upon categorization. However, defining features can rarely be found for categories in ...