This paper introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; for example, the linear usage of imperative features such as state and/or continuations. The enriched effect calculus is implemented as an extension o...

We provide a new characterization of enriched accessible categories by introducing the two notions virtual reflectivity and orthogonality as generalization usual conditions for locally presentable categories. The word refers to fact that are given in free completion V-category involved under small limits, instead itself. In this way we hope clearer understanding theory well useful recognizing V...

In this paper, we focus on the Data Envelopment Analysis (DEA)-based model structures have been used in assessing bank branch efficiency. Probing the methodologies of 75 published studies at the branch level since 1985 to early 2015, we found that these models can be divided into four categories: standard basic DEA models, single level and multi-level models, enriched (hybrid) models and specia...

There is a 2-category J -Colim of small categories equipped with a choice of colimit for each diagram whose domain J lies in a given small class J of small categories, functors strictly preserving such colimits, and natural transformations. The evident forgetful 2-functor from J -Colim to the 2-category Cat of small categories is known to be monadic. We extend this result by considering not jus...

Chu connections and back diagonals are introduced as morphisms for distributors between categories enriched in a small quantaloid Q. These notions, meaningful for closed bicategories, dualize the constructions of arrow categories and the Freyd completion of categories. It is shown that, for a small quantaloid Q, the category of complete Q-categories and left adjoints is a retract of the dual of...

In this paper we consider Milner’s calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We define operational notions of preorder and equivalence as probabilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...

These notes were written to accompany two talks given in the Algebraic Topology and Category Theory Proseminar at the University of Chicago in Winter 2009. When a category has some notion of limits and colimits associated to it, its ordinary limits and colimits are not necessarily homotopically meaningful. We describe a notion of a “homotopy colimit” for two sorts of categories with a homotopy ...

Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched with notions such as approximation by computation or representability. The latter are commonly studied in denotational semantics and domain theory and captured...

The order-enriched category of monotonic predicate transformers over posets is a model of the reenement calculus of higher order imperative programs and pre-post speciications. This category is shown to be equivalent to the category of spans over ideal relations, and ideal relations are shown to be spans over monotonic functions between posets, using a skew span construction because the standar...

The question of how to model {calculus name passing has attracted signiicant interest. Here, this topic is approached with a new fully abstract interleaving model. Its central feature: Every semantic object contains all its transformations under injective name replacements. It is shown how this enrichment can be used, in a systematic way, to obtain compositional interpretations of the construct...