This investigation will use this ability in a different way. Studies have shown that a category can create a grade structure of prototypical items. We will take a graded structure generated by a category, and see if we can recreate the category based on presenting prototypical examples in a variety of ways. Five different sampling techniques will be used to determine which one is the best for category reconstruction. Since the items themselves have bits of information about the category, the number of samples presented will also be manipulated to determine if this is a factor in determining the category. The independent variables investigated were: sampling technique, and prompt conditions. In determining the effect of the independent variables on matching a category, the independent variables were also considered as mediating variables of each other. The method of opportunistic sampling was used for the surveys. The main participants were undergraduate 3rd year students taking a MSci 311 course at the University of Waterloo. Results indicate that there was no statistical significance. Fluctuations in significance levels indicate some random findings. Participants are not discriminating the samples or prompts which were given. This research is a contribution to this field because little research has been conducted in this area and implications are drawn for future research on the saliency of a category or attribute that can vary by context or knowledge

The brief introductory chapter attempts to motivate the project by pointing to (a) the intuitive appeal and importance of the notion of an object (that is, a “paradigmatic” individual), and (b) the need – for the sake of progress in at least two important debates in ontology – to replace this notion with a series of related notions of individuals of different sorts. Section One of Chapter Two aims to accomplish two primary tasks. The first is to clarify the intensions of three often employed but ambiguous categorical terms: ‘individual’, ‘particular’ and ‘object’, with emphasis on the third, which is often taken to be of particular philosophical significance. I carry out this clarificatory task by weighing various positions in the literature and arguing for explications of each notion that are maximally economical and neutral, that is, explications which (a) overlap as little as possible with other important ontological notions and (b) do not require us to take a stand on any apparently intractable (but not directly relevant) debates (e.g. on the problem of realism vs. nominalism about universals). The second task of 2.1 is to delineate the various ontological distinctions that will be turned, in Chapter Four, into the “dimensions” of which the ontological framework I will be advocating there is composed. The delineation of these distinctions takes place naturally in the course of attempting to characterize the notion of an object (an intrinsically unified, independent concrete particular) and to distinguish it from the notions of an individual and a particular, in spite of the fact that objects are both individuals and particulars. In the second section of Chapter Two I illustrate the centrality of the notion of an object in Ontology by showing how that notion figures in the debate over the existence of artifacts. I argue that progress in this debate has been hindered by the way it has been framed, and that seeing the issue as concerning not whether artifacts exist but whether artifacts are objects (in the sense outlined in 2.1) enables us to better appreciate and accommodate the different perspectives of the debate’s participants. At the same time, this way of dissolving the dispute makes clear that existence is not limited to entities that fall under the relevant concept of an object, foreshadowing the pluralistic ontological framework to be developed in Chapter Four. Chapter Three pronounces on a second debate in ontology, in which three positions concerning the correct ontological assay of the class of intrinsically unified independent concrete particulars (objects) are in competition with each other. My conclusion is that none of the three positions succeeds, since each faces fairly serious difficulties. I suggest that the (or at least one major) root of our inability to locate the correct ontological assay is the inclination to treat all ontologically significant entities as objects in the indicated sense, and the corresponding inclination to attempt to give an ontological assay that covers all objects, neglecting important differences between distinct types of individuals. Chapter Four begins by displaying in greater detail the considerations (canvassed very briefly in the introductory chapter) that make the notion of an object appear to be indispensible. However, the results of the second section of Chapter Two and of the entirety of Chapter Three have already shown two areas in which the notion of an object tends to lead to confusion. So a tension emerges between the prima facie necessity of the notion and the reasons we have found for thinking that this notion either is itself problematic or at least tends to cause problems for other issues in Ontology. The remainder of Chapter Four consists in explaining my strategy for moving forward. Briefly, this strategy involves replacing the notion of an object with a series of concepts applicable to individuals of various types. Each of the components belonging to a given “individual-concept” is drawn from one or another side of one of the ontological distinctions that together form an overall ontological framework, and which components are involved is a matter to be determined by examining the conceptual demands imposed by the various practices (explanatory or otherwise) which we engage in, that require us to appeal to individuals of the type in question. The resulting “pluralistic” ontological framework provides a way of situating and relating types of individuals that both avoids the confusions that the single general concept of an object leads to, and is capable of indicating the varying degrees of “ontological robustness” or “object-like-ness” of any given type of individual. I conclude by suggesting how the framework I am advocating can be elaborated on and put to use in further research.

Over the decades, brand extension has been a core marketing strategy for a great number of companies. Brand extension enjoys a good reputation for bringing practical advantages to companies whilst it faces disputation at the same time because of a relatively high percentage of failures. Using modified Aaker’s brand equity model as the theoretical framework, the authors undertake a comparative case study to analyze the opportunities and challenges a company might face while using brand extension strategy, particularly in category brand extension: Yamaha Corporation as a successful example, and Virgin Group as a failure one. The analysis mainly focuses on the four elements in the modified Aaker’s brand equity model: brand awareness, brand loyalty, brand associations and perceived quality. The findings show that a company faces challenges when consumers have a more solid loyalty towards the competitor’s brand and when consumers are confused about brand associations. On the contrary, a company acquires opportunities in brand extension as long as a strong brand loyalty and a related connection between the parent brand and the extended brand exist.

<p>In this thesis we try to construct a stability condition on the quintic threefold. We have not succeeded in proving the existence of such a stability condition. However we have constructed a stability condition on a quotient category of projective space that approximates the quintic. We conjecture the existence of a stability condition on the quintic threefold generated by spherical objects and explore some consequences.</p> / Dissertation

This thesis introduces the infinitesimal symmetries of Dixmier-Douady gerbes over smooth manifolds. The collection of these symmetries are the counterpart for gerbes of the Lie algebra of circle invariant vector fields on principal circle bundles, and are intimately related to connective structures and curvings. We prove that these symmetries possess a Lie 2-algebra structure, and relate them to equivariant gerbes via a "differentiation functor". We also explain the relationship between the infinitesimal symmetries of gerbes and other mathematical structures including Courant algebroids and the String Lie 2-algebra. / text

Supplier integration in category management means that a supplier takes part in the activities that are traditionally performed by retailers. These activities are the selection of which products to sell, decisions on how to price and market the products, and making sure that the products are delivered to the stores in a timely manner. Depending on the situation, an integration of suppliers in these activities can be more or less suitable. As more research is needed to understand when supplier integration in category management is suitable, the purpose of this thesis is to describe and analyze how situational factors affect the relationship consequences of supplier integration in category management. Specifically, the relationship consequences are expressed in terms of relationship performance and interdependence between the firms. The study builds on empirical data about British and Swedish builders’ merchants and their suppliers, with a particular focus on timber suppliers. Data has mainly been collected through participative observations and interviews. Five situational factors that improve the relationship performance of supplier integration in category management are identified: large retailer firms, supplier product knowledge, homogeneity of market demands for the supplier’s products, mutual trust and a shared view on customer value between the supplier and retailer. Three situational factors are identified that affect the interdependence between the retailer and the supplier when supplier integration in category management is implemented: supplier product knowledge, whether the supplier or the retailer initiates the integration and whether coercive or non-coercive power has to be used in the implementation. This thesis contributes to retail literature by highlighting the need to include situational factors in the analysis of supplier integration, clarifying which activities are comprised by category management and suggesting a theoretical foundation based on the resource-based view and the transaction cost framework to analyse relationship performance in retailer-supplier dyads. When making decisions on integration, managers of retailers and their suppliers are advised to consider the fit with their overall strategy, the fit with the surrounding situation and the effects both in terms of interdependence and relationship performance.

In 1997, Drs. G. R. Blakley and I. Borosh published two papers whose stated purpose was to present a general formulation of the notion of a code that depends only upon a code's structure and not its functionality. In doing so, they created a further generalization--the idea of a precode. Recently, Drs. Blakley, Borosh, and A. Klappenecker have worked on interpreting the structures and results in these pioneering papers within the framework of category theory. The purpose of this dissertation is to further the above work. In particular, we seek to accomplish the following tasks within the ``general theory of codes.' 1. Rewrite the original two papers in terms of the alternate representations of precodes as bipartite digraphs and Boolean matrices. 2. Count various types of bipartite graphs up to isomorphism, and count various classes of codes and precodes up to isomorphism. 3. Identify many of the classical objects and morphisms from category theory within the categories of codes and precodes. 4. Describe the various ways of constructing a code from a precode by ``splitting' the precode. Identify important properties of these constructions and their interrelationship. Discuss the properties of the constructed codes with regard to the factorization of homomorphisms through them, and discuss their relationship to the code constructed from the precode by ``smashing.' 5. Define a parametrization of a precode and give constructions of various parametrizations of a given precode, including a ``minimal' parametrization. 6. Use the computer algebra system, Maple, to represent and display a precode and its companion, opposite, smash, split, bald-split, and various parametrizations. Implement the formulae developed for counting bipartite graphs and precodes up to isomorphism.

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, Petri nets, chemical reaction networks, and so on. The key feature is that the language is comprised of a number of components with multiple (input/output) terminals, each possibly labelled with some type, that may then be connected together along these terminals to form a larger network. The components form hyperedges between labelled vertices, and so a diagram in this language forms a hypergraph. We formalise the compositional structure by introducing the notion of a hypergraph category. Network-style diagrammatic languages and their semantics thus form hypergraph categories, and semantic interpretation gives a hypergraph functor. The first part of this thesis develops the theory of hypergraph categories. In particular, we introduce the tools of decorated cospans and corelations. Decorated cospans allow straightforward construction of hypergraph categories from diagrammatic languages: the inputs, outputs, and their composition are modelled by the cospans, while the 'decorations' specify the components themselves. Not all hypergraph categories can be constructed, however, through decorated cospans. Decorated corelations are a more powerful version that permits construction of all hypergraph categories and hypergraph functors. These are often useful for constructing the semantic categories of diagrammatic languages and functors from diagrams to the semantics. To illustrate these principles, the second part of this thesis details applications to linear time-invariant dynamical systems and passive linear networks.

The Master´s Thesis deals with the category management on the supplier´s side. The main objective of the thesis is to find the best shelf optimization for the selected categories. In the theoretical part there are defined the main terms and the category management process. The analytical part is then focused on the whole category management process in Albert. The analytical part is based on primary and secondary data. The primary data consists of quantitative questionnaire, observation and interview with customers. The secondary data are based on MML-TGI research, GfK reports and Nielsen reports. In the thesis there is a big emphasis on the customer shopping behaviour. At the end of the thesis there are given shelf proposals and recommendations to the retailer.

This paper provides two generalizations of differential and integral categories: Leibniz and generalized Rota-Baxter categories, which capture certain algebraic structures, and q-categories, which capture structures of quantum calculus. In the search for new examples of differential and integral categories, it was observed that many structures were not quite examples but satisfied certain properties and not others. This leads us to the definition of Leibniz, Rota-Baxter and proto-FTC categories. In generalizing Rota-Baxter categories further to an arbitrary weight, we show that we recapture Ribenboim's generalized power series as a monad on vector spaces with a generalized integral transformation. This also subsumes the renormalization operator on Laurent series, which has applications in the quantum realm. Finally, we define quantum differential and quantum integral categories, show that they recapture the usual notions of quantum calculus on polynomials, and construct a new example to indicate their potential usefulness outside of that specific setting