vi, 85 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We define and study a gluing procedure for Bridgeland stability conditions in the situation where a triangulated category has a semiorthogonal decomposition. As one application, we construct an open, contractible subset U in the stability manifold of the derived category [Special characters omitted.] of [Special characters omitted.] -equivariant coherent sheaves on a smooth curve X , associated with a degree 2 map X [arrow right] Y , where Y is another curve. In the case where X is an elliptic curve we construct an open, connected subset in the stability manifold using exceptional collections containing the subset U . We also give a new proof of the constructibility of exceptional collections on [Special characters omitted.] . This dissertation contains previously unpublished co-authored material. / Committee in charge: Alexander Polishchuk, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Victor Ostrik, Member, Mathematics; Brad Shelton, Member, Mathematics; Michael Kellman, Outside Member, Chemistry

We construct categories of spectra for two model categories. The first is the category of small categories with the canonical model structure, and the second is the category of directed graphs with the Bisson-Tsemo model structure. In both cases, the category of spectra is homotopically trivial. This implies that the Goodwillie derivatives of the identity functor in each category, if they exist, are weakly equivalent to the zero spectrum. Finally, we give an infinite family of model structures on the category of small categories.

Nas ultimas décadas, houve um aumento na diversidade do perfil dos moradores bem como nos seus requisito específicos em decorrência de mudanças no estilo de vida contemporâneo. Tais mudanças vem tornando a provisão tradicional de habitações padronizadas inadequadas e demandam o desenvolvimento de estratégias de customização capazes de responder aos requisitos específicos dos moradores. Neste contexto, a abordagem da customização em massa (CM) e conceitos relacionados pode potencialmente aumento o valor do produto habitacional através do atendimento dos requisitos específicos do moradores. Apesar disto, a literatura é ainda limitada em termos de estudos que auxiliem organizações a desenvolver estratégias de customização, especialmente no setor habitacional. Visando responder este problema de pesquisa, esta investigação adota a abordagem da design science. Esta abordagem tem por objetivo desenvolver soluções (artefatos, modelos, software, entre outros) que resolvam problemas práticos e ao mesmo tempo tenham potencial para uma contribuição teórica. A solução desenvolvida nesta pesquisa é um modelo conceitual com categorias de decisão para definição de estratégias de customização no contexto habitacional. O modelo contém dez categorias de decisão, que definem o escopo de uma estratégia de customização e abordam aspectos relacionados a interface com o cliente, design do produto, e operações. Outros resultados da pesquisa, além deste modelo, incluem implementações (operacionalizações que demonstram que a solução funciona), avaliação da utilidade da solução, e avaliação da contribuição teórica da solução. O processo de pesquisa envolveu etapas chave da design science: encontrar um problema prático e com potencial para contribuição teórica, obter um entendimento deste problema, desenvolver uma solução, testar a solução, avaliando sua utilidade, e avaliar a contribuição teórica desta solução. Quatro estudos de caso com organizações envolvidas no setor da construção habitacional (no Brasil e no Reino Unido) também foram desenvolvidos. Em termos da contribuição teórica do modelo, algumas categorias (classes de itens, combinações de módulos, unidades de customização, e sequências de configuração) foram desenvolvidas com base em dados empíricos e constituem nova conceitualizações relacionadas a abordagem da CM que podem ser usadas no desenvolvimento de estratégias de customização. Outras categorias (espaço de solução, interface entre módulos, ponto de entrada do pedido, tipos de customização, e abordagens de visualização) baseiam-se em conceitos já disponíveis na literatura. A contribuição destas categorias é adaptar tais conceitos, através da proposição de constructos, visando facilitar a aplicação dos mesmos na definição de estratégias de customização. / There has been an increasing diversity on dwellers profiles and on their requirements in the last few decades, due to major changes in contemporary lifestyles. Such changes are making the traditional provision of standardised houses inadequate, requiring the development of new strategies able to provide customised dwellings. In this context, the application of the mass customisation (MC) approach and related concepts can potentially increase the value of housing through the fulfilling of the specific requirements of dwellers. In spite of that, the literature on the MC approach is limited in providing guidance to organisations in developing customisation strategies, particularly in the house-building sector. In order to address such a problem, a design science approach is adopted in this investigation. Such an approach deals with the construction of solutions (artefact, models, software, among other) for problems with practical relevance and potential for theoretical contribution. The solution devised in this investigation is a conceptual framework to be used by organisations of the house-building sector in defining customisation strategies. The framework entails ten decision categories that define the scope of a customisation strategy and also address some aspects of the clients’ interfaces, product design, and operations areas. Other outputs of this research include (i) instantiations (implementations that demonstrate that the solution works), (ii) evaluation of the solution utility, and (iii) evaluation of the theoretical contribution of the solution. The research process undertaken involved keys steps of the design science approach: find a practical problem with potential for a theoretical contribution, obtain an understanding of such a problem, develop a solution, test the solution and evaluate its utility, and assess the theoretical contribution of the solution. Four case studies with organisations (in Brazil and in the U.K.) of the house-building sector were also carried out and were particularly important in the solution devising and solution testing steps. In terms of theoretical contribution of the solution, some of the categories developed (classes of items, module combinations, customisation units, and configuration sequence) are grounded on empirical data and provide new conceptualisations related to the MC approach and which can be used in defining customisation strategies. Other categories (solution space, modules, module interfaces, order penetration point, types of customisation, and visualisation approaches) rely on existing concepts and underpinnings available on the literature on the MC approach. The main contribution of those categories is to adapt such concepts by proposing operational constructs, enabling such knowledge to be more applicable in devising customisation strategies.

We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.

The main theme of the thesis is to present and compare three different viewpoints on semi-abelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories coincide whenever they are both defined, but having these different approaches available makes it possible to choose the most appropriate one in any given situation, and their respective strengths complement each other to give powerful homological tools. The oldest viewpoint, which is borrowed from the abelian context where it was introduced by Barr and Beck, is comonadic homology, generating projective simplicial resolutions in a functorial way. This concept only works in monadic semi-abelian categories, such as semi-abelian varieties, including the categories of groups and Lie algebras. Comonadic homology can be viewed not only as a functor in the first entry, giving homology of objects for a particular choice of coefficients, but also as a functor in the second variable, varying the coefficients themselves. As such it has certain universality properties which single it out amongst theories of a similar kind. This is well-known in the setting of abelian categories, but here we extend this result to our semi-abelian context. Fixing the choice of coefficients again, the question naturally arises of how the homology theory depends on the chosen comonad. Again it is well-known in the abelian case that the theory only depends on the projective class which the comonad generates. We extend this to the semi-abelian setting by proving a comparison theorem for simplicial resolutions. This leads to the result that any two projective simplicial resolutions, the definition of which requires slightly more care in the semi-abelian setting, give rise to the same homology. Thus again the homology theory only depends on the projective class. The second viewpoint uses Hopf formulae to define homology, and works in a non-monadic setting; it only requires a semi-abelian category with enough projectives. Even this slightly weaker setting leads to strong results such as a long exact homology sequence, the Everaert sequence, which is a generalised and extended version of the Stallings-Stammbach sequence known for groups. Hopf formulae use projective presentations of objects, and this is closer to the abelian philosophy of using any projective resolution, rather than a special functorial one generated by a comonad. To define higher Hopf formulae for the higher homology objects the use of categorical Galois theory is crucial. This theory allows a choice of Birkhoff subcategory to generate a class of central extensions, which play a big role not only in the definition via Hopf formulae but also in our third viewpoint. This final and new viewpoint we consider is homology via satellites or pointwise Kan extensions. This makes the universal properties of the homology objects apparent, giving a useful new tool in dealing with statements about homology. The driving motivation behind this point of view is the Everaert sequence mentioned above. Janelidze's theory of generalised satellites enables us to use the universal properties of the Everaert sequence to interpret homology as a pointwise Kan extension, or limit. In the first instance, this allows us to calculate homology step by step, and it removes the need for projective objects from the definition. Furthermore, we show that homology is the limit of the diagram consisting of the kernels of all central extensions of a given object, which forges a strong connection between homology and cohomology. When enough projectives are available, we can interpret homology as calculating fixed points of endomorphisms of a given projective presentation.

Relative terms are those such as ‘larger’, ‘smaller’, ‘parent’ and ‘offspring’. Questions concerning the nature of this type of term in Plato fall under three themes. First, logic: what is the syntax and semantics of relative terms? Second, metaphysics: what structures in the world constitute relative properties? Third, taxonomy: do relative terms form a distinguishable class? Questions concerning purpose ask what role these terms have in the wider economy of Plato’s thought. Only one existing approach addresses all of these themes and questions: it was put forward by G.E.L. Owen in 1957, although it was subsequently developed by others. The Owenian view holds that relatives are syntactically or semantically incomplete, that they are identical to metaphysically dyadic relations and that they do form a taxonomic class. According to Owen, Plato introduces relative terms to bolster a certain argument for the separation of forms and participants. Therefore, they have an ontological purpose. This thesis aims to offer a plausible, non–anachronistic alternative to the Owenian view. To give such an account I have to argue for a radically different logic, metaphysics and purpose for relatives in Plato. I call the view that I defend ‘conjunctivism’. I begin by characterising the logic of conjunctivism. Plato holds that relative terms have formal objects. These are exceptionlessly correct objects of the relative in question. A parent is always and only parent of offspring, so ‘offspring’ is the formal object of ‘parent’. I then demonstrate that the metaphysical problems for relatives which are not dyadic relations are avoided by Plato’s version of conjunctivism. Looking at Sophist 255c–d and Parmenides 133c–134e, I discuss the taxonomy of relative terms. I show that, under the conjunctive reading, they form a distinguishable class and, in contrast to Owenian relatives, each reciprocates with its correlative. So, just as a parent is relative to offspring, so offspring are relative to a parent. With the nature of relative terms established, I proceed to refute Owen’s account of their purpose, and give my own explanation. By looking at passages from the Euthydemus and Charmides, I argue that Plato introduced relative terms to articulate why some arguments are fallacies and others not. That is, relative terms have a dialectical purpose.

Traditional recursion theory is the study of computable functions on the natural numbers. This thesis considers recursion theory in first-order arithmetical theories and categories, thus expanding the work of Ritchie and Young, Lambek, Scott, and Hofstra. We give a complete characterisation of the representability of computable functions in arithmetical theories, paying attention to the differences between intuitionistic and classical theories and between theories with and without induction. When considering recursion theory from a category-theoretic perspective, we examine syntactic categories of arithmetical theories. In this setting, we construct a strong parameterised natural numbers object and give necessary and sufficient conditions to construct a Turing category associated to an intuitionistic arithmetical theory with induction.

Both myths and theories have, over time, been involved in shaping the importance of what leadership can mean. The depth devoted to leadership, the more complex the concept becomes. Power is also an abstract concept and should be included when studying leadership. Furthermore, several researchers ask the question whether a female leader can be considered without being related to the man. With this as a background, the purpose of the study has been founded, which is to study the beliefs that leaders in a managerial position have about leadership and power. We also want to illustrate whether these performances differ depending on whether the leader in the management position is a man or woman. In order to be able to answer this, the concepts of leadership, power and gender are concretized in the theoretical frame of reference. Furthermore, the previous research focuses on studies carried out with the aim of highlighting gender differences within organizations. The study is based on a qualitative method based on six semi-structured interviews. The results of the study show that there is a context that determines which leadership should prevail and that differences in beliefs about leadership and power exist between male and female leaders in a management position. / Såväl myter som teorier har genom tiden varit med och format betydelsen av vad ledarskap kan innebära. Ju mer fördjupning som ägnas åt ledarskap, desto mer komplex blir begreppet. Makt är även det ett abstrakt begrepp och bör inkluderas när ledarskap studeras. Vidare ställer flertal forskare frågan om en kvinnlig ledare kan beaktas utan att sättas i relation till mannen. Med detta som bakgrund har studiens syfte grundats, vilket är att studera föreställningar som ledare i en chefsposition har kring ledarskap och makt. Vi vill även åskådliggöra om dessa föreställningarna skiljer sig åt beroende på om ledaren i chefspositionen är en man eller kvinna. För att kunna besvara detta konkretiseras begreppen ledarskap, makt och kön i den teoretiska referensramen. Vidare fokuserar den tidigare forskningen på studier som utförts i syfte att belysa könsskillnader inom organisationer. Studien utgår från en kvalitativ metod som bygger på sex stycken semistrukturerade intervjuer. Studiens resultat visar på att det är kontext som bestämmer vilket ledarskap som skall råda samt att skiljaktigheter i föreställningar om ledarskap och makt finns mellan manliga- och kvinnliga ledare i en chefsposition.

Thesis(M. Sc. (Mathematics)) -- University of Limpopo, 2021 / A Cs´ asz´ ar frame is a point free version of syntopogenous space, itself a concept that is attributed to ´ Akos Cs´ asz´ ar [14]. In his two papers, Chung ([12] and [13]) characterised few types of Cs´ asz´ ar frames and extended Hong’s construction [21] to the Cauchy completions in Cs´ asz´ ar frames. From his results, we anchored objectives of our study on the actions of certain frame homomorphisms on proximal Cs´ asz´ ar frames, as well as co-reflective subcategories of Cauchy complete Cs´ asz´ ar frames. We conclude the dissertation by constructing the compactification of proximal Cs´ asz´ ar frames by applying the methods of Banaschewski and Mulvey [7]. We introduce a weak notion of connectedness of Cs´ asz´ ar frames and show, following the approach of Baboolal and Banaschewski [4], that most of the standard results on connectedness are do-able in the setting of Cs´asz'ar.

This dissertation seeks to examine the essential nature of time--both the concept in physics, biology, and philosophy, and the phenomenon in life and culture--with the ultimate goal of deepening our understanding of the empirical manifestation of time in human mental experience. It thus engages with both philosophy and with empirical science, natural as well as humanistic, in the paradigms of history, social theory, fundamental (or philosophical) anthropology, as well as with human neuroscience. The central argument is that while time is not an empirical phenomenon in physics - time itself is not an absolute quality of matter - one can make a certain argument for the real existence of time in biology, and still a different argument for a unique, linear phenomenon of time that derives from the specific human, cultural, experience. To make these arguments the dissertation devotes attention to the analysis of both the concept of time and the empirical phenomenon to which it refers successively in physics, biology, philosophy and history/sociology. Arriving at the conclusion that the linear concept of time (the causally significant relationship between the past, present and future) reflects a phenomenon that is uniquely human and suggests the ways in which this experience is necessarily reflected in the brain. / 2022-02-26T00:00:00Z