In this paper we re-develop the foundations of the category theory of quasicategories (also called ∞-categories) using 2-category theory. We show that Joyal’s strict 2-category of quasi-categories admits certain weak 2-limits, among them weak comma objects. We use these comma quasi-categories to encode universal properties relevant to limits, colimits, and adjunctions and prove the expected the...

Abstract We introduce the theory of enrichment over an internal monoidal category as a common generalization both standard theories enriched and categories. Then, we contextualize new notion by comparing it to another known enrichment: that for indexed It turns out two notions are closely related.

This survey paper, specifically targeted at a readership of fuzzy logicians and fuzzy set theorists, aims to provide a gentle introduction to the basic notions of quantaloidenriched category theory. We discuss at length the definitions of quantaloid, quantaloidenriched category, distributor and functor, always giving several examples that – hopefully – appeal to the intended readership. To indi...

Given a horizontal monoid M in a duoidal category F , we examine the relationship between bimonoid structures on M and monoidal structures on the category F ∗M of right M -modules which lift the vertical monoidal structure of F . We obtain our result using a variant of the so-called Tannaka adjunction; that is, an adjunction inducing the equivalence which expresses Tannaka duality. The approach...

In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effect-free coalgebraic operational semantics, given by a natural transformation of syntax over behaviour. The operational semantics of the extended language arises by distributing program syntax over effects, again inducing a coalgebraic operational semantics, but this time...

This study examined the relationship between phonemic and semantic (category) verbal fluency and cognitive status in the Wisconsin Registry for Alzheimer's Prevention (WRAP), a longitudinal cohort enriched for family history of Alzheimer's disease. Participants were 283 WRAP subjects (age 53.1[6.5] years at baseline); who had completed three waves of assessment, over ∼6 years and met psychometr...

Chu connections and back diagonals are introduced as morphisms for distributors between categories enriched in a small quantaloid Q. These constructions, meaningful for closed bicategories, are dual to that 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 th...

Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures based on a set of complex query computations. They express the semantics of view-based mappings between databases. The higher (logical) level scheme mappings b...

The behavioural and cognitive effects of oligofructose-enriched inulin at the doses of 5 and 10 % in the diet, orally ingested daily during 2 weeks, were investigated using a functional observational battery (FOB) and the light extinction test in male Wistar rats. Control rats received a standard diet and were tested in the same test situations. The behavioural effects were assessed 2 d before ...

Address for Correspondence: Dr. Eren Fatma Akçıl, İstanbul Üniversitesi Cerrahpaşa Tıp Fakültesi, Anesteziyoloji ve Reanimasyon Anabilim Dalı, İstanbul, Türkiye Phone: +90 212 414 30 00-21248 E-mail: [email protected] ©Copyright 2015 by Turkish Anaesthesiology and Intensive Care Society Available online at www.jtaics.org Received : 09.10.2014 Accepted : 17.11.2014 Eren Fatma Akçıl, Özlem Korkma...