Products in categories of relations

AbstractThe relational product construction is often consider as an abstract version of cartesian products. The existence of those products is strongly connected with the representability of that category. In this paper we investigate a canonical weakening of the notion of a relational product. Unlike the strong version, any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we provide several examples, and we study the categorical properties of the new construction

Weak n-Ary Relational Products in Allegories

Allegories are enriched categories generalizing a category of sets and binary relations. Accordingly, relational products in an allegory can be viewed as a generalization of Cartesian products. There are several definitions of relational products currently in the literature. Interestingly, definitions for binary products do not generalize easily to n-ary ones. In this paper, we provide a new definition of an n-ary relational product, and we examine its properties.We would like to thank the reviewers for their helpful suggestions

Topological Ramsey spaces from Fra\"iss\'e classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fra\"iss\'e classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Soki\v{c} is extended to equivalence relations for finite products of structures from Fra\"iss\'e classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the Pudl\'ak-R\"odl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fra\"iss\'e classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor in \cite{Baumgartner/Taylor78} generating p-points which are $k$-arrow but not $k+1$-arrow, and in a partial order of Blass in \cite{Blass73} producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of $n$ many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra $\mathcal{P}(n)$. If the number of Fra\"iss\'e classes on each block grows without bound, then the Tukey types of the p-points below the space's associated ultrafilter have the structure exactly $[\omega]^{<\omega}$. In contrast, the set of isomorphism types of any product of finitely many Fra\"iss\'e classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template.Comment: 35 pages. Abstract and introduction re-written to make very clear the main points of the paper. Some typos and a few minor errors have been fixe

Groupoids, Frobenius algebras and Poisson sigma models

In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius algebras in the category Rel, as well as an adjunction between a special type of semigroupoids and relative H*-algebras. The connection between groupoids and Frobenius algebras is made explicit by introducing what we called weak monoids and relational symplectic groupoids, in the context of Poisson sigma models with boundary and in particular, describing such structures in the ex- tended symplectic category and the category of Hilbert spaces. This is part of a joint work with Alberto Cattaneo and Chris Heunen.Comment: 12 pages, 1 figure. To appear in "Mathematical Aspects of Quantum Field Theories". Mathematical Physical Studies, Springer. Proceedings of the Winter School in Mathematical Physics, Les Houges, 201

An investigation into the relationship between customer relationship marketing and customer retention: superstore retailing context in Bangladesh

The context of this study is Bangladesh`s food retailing sector. The main purpose of this study is to investigate the relationship between Customer Relationship Marketing (CRM) and customer retention. The core aim of Relationship Marketing is to build long lasting mutually bonded relationships with customers and various other important stakeholders. The concept has attracted considerable attention among scholars in recent decades and has appeared in service marketing literature as a new marketing paradigm. The concept is critical to the success of any organisation as it has been an accepted phenomenon that maintains that existing customers are far easier to retain than is the process of acquiring new customers. In order to stay in business and cope with the challenging business dynamism, organisations are continuously searching for reliable and serviceable strategies to be employed in order to increase customer retention. However, there is a lack of consensus among researchers on the core antecedents of relationship marketing that can be used to achieve the above aims, especially while the concept is new in the context of organised retailing sectors in Bangladesh. In response, the study developed a conceptual framework of customer retention strategy which incorporates bonds, service quality and relational quality into one relationship model. The model establishes eleven hypotheses. A sample of 202 grocery food retail customers were selected in a random sample from four selected superstores. The results support hypothesized relationships built on the model. The findings indicate that service quality, trust, bond and customer satisfactions are vital for creating positive customer loyalty which in turn creates customer retentionPeer reviewedFinal Published versio

Indexed Induction and Coinduction, Fibrationally

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a dual to the sound induction rule for inductive types that we developed previously. That is, we present a sound coinduction rule for any data type arising as the carrier of the final coalgebra of a functor, thus relaxing Hermida and Jacobs' restriction to polynomial functors. To achieve this we introduce the notion of a quotient category with equality (QCE) that i) abstracts the standard notion of a fibration of relations constructed from a given fibration; and ii) plays a role in the theory of coinduction dual to that played by a comprehension category with unit (CCU) in the theory of induction. Secondly, we show that inductive and coinductive indexed types also admit sound induction and coinduction rules. Indexed data types often arise as carriers of initial algebras and final coalgebras of functors on slice categories, so we give sufficient conditions under which we can construct, from a CCU (QCE) U:E \rightarrow B, a fibration with base B/I that models indexing by I and is also a CCU (resp., QCE). We finish the paper by considering the more general case of sound induction and coinduction rules for indexed data types when the indexing is itself given by a fibration

Building Intellectual Capital in Incubated Technology Firms

Purpose: The value of relational capital generated by entrepreneurs with their internal and external environment (Hormiga, Batista-Canino and Sanchez-Medina, 2011), provides considerable resources when properly leveraged. It is particularly important in environments such as the high tech sector of incomplete information and weak economic markets such as new products, markets or technologies (Davidsson, and Honig, 2003). The paper examines how incubated technology entrepreneurs build relational capital for a new venture formation in the social context of a Higher Education Institution. Design/methodology/approach: Our study took a qualitative approach based on content analysis of business plans and in-depth interviews with twenty-five technology entrepreneurs on an incubation programme – South East Enterprise Platform Programme - for technology graduates in the South East of Ireland. Findings: Our study found that technology entrepreneurs during new venture formation engaged in four types of relational capital activities, namely, development of networks and contacts, relationship building, accessing and leveraging knowledge experts and members of associations. Practical Implications: Incubator programmes need to actively support social building activities of technology entrepreneurs. HEI knowledge assets and networks are critical elements in supporting incubator technology entrepreneurs. Originality/Value: Our study identified four types of relational capital building. We also found using Evans Jones (1995) categorization of technology entrepreneurs that users, producers, opportunists and non–technical entrepreneurs engaged in client focused relational capital building, whereas researcher types networked with service providers and displayed arms length relational capital building styles

The Dark Energy Survey Data Management System

The Dark Energy Survey collaboration will study cosmic acceleration with a 5000 deg2 griZY survey in the southern sky over 525 nights from 2011-2016. The DES data management (DESDM) system will be used to process and archive these data and the resulting science ready data products. The DESDM system consists of an integrated archive, a processing framework, an ensemble of astronomy codes and a data access framework. We are developing the DESDM system for operation in the high performance computing (HPC) environments at NCSA and Fermilab. Operating the DESDM system in an HPC environment offers both speed and flexibility. We will employ it for our regular nightly processing needs, and for more compute-intensive tasks such as large scale image coaddition campaigns, extraction of weak lensing shear from the full survey dataset, and massive seasonal reprocessing of the DES data. Data products will be available to the Collaboration and later to the public through a virtual-observatory compatible web portal. Our approach leverages investments in publicly available HPC systems, greatly reducing hardware and maintenance costs to the project, which must deploy and maintain only the storage, database platforms and orchestration and web portal nodes that are specific to DESDM. In Fall 2007, we tested the current DESDM system on both simulated and real survey data. We used Teragrid to process 10 simulated DES nights (3TB of raw data), ingesting and calibrating approximately 250 million objects into the DES Archive database. We also used DESDM to process and calibrate over 50 nights of survey data acquired with the Mosaic2 camera. Comparison to truth tables in the case of the simulated data and internal crosschecks in the case of the real data indicate that astrometric and photometric data quality is excellent.Comment: To be published in the proceedings of the SPIE conference on Astronomical Instrumentation (held in Marseille in June 2008). This preprint is made available with the permission of SPIE. Further information together with preprint containing full quality images is available at http://desweb.cosmology.uiuc.edu/wik