In thinking about quantum causality one would like to approach rigorous QFT from outside the perspective of QFT, which one expects to recover only in a specific physical domain of quantum gravity. This thesis considers issues in causality using Category Theory, and their application to field theoretic observables. It appears that an abstract categorical Machian principle of duality for a ribbon graph calculus has the potential to incorporate the recent calculation of particle rest masses by Brannen, as well as the Bilson-Thompson characterisation of the particles of the Standard Model. This thesis shows how Veneziano n point functions may be recovered in such a framework, using cohomological techniques inspired by twistor theory and recent MHV techniques. This distinct approach fits into a rich framework of higher operads, leaving room for a generalisation to other physical amplitudes. The utility of operads raises the question of a categorical description for the underlying physical logic. We need to consider quantum analogues of a topos. Grothendieck's concept of a topos is a genuine extension of the notion of a space that incorporates a logic internal to itself. Conventional quantum logic has yet to be put into a form of equal utility, although its logic has been formulated in category theoretic terms. Axioms for a quantum topos are given in this thesis, in terms of braided monoidal categories. The associated logic is analysed and, in particular, elements of linear vector space logic are shown to be recovered. The usefulness of doing so for ordinary quantum computation was made apparent recently by Coecke et al. Vector spaces underly every notion of algebra, and a new perspective on it is therefore useful. The concept of state vector is also readdressed in the language of tricategories.

Thesis (Ph. D.)--Miami University, Dept. of Psychology, 2009. / Title from second page of PDF document. Includes bibliographical references (p. 26-31).

Zugl.: Marburg, Univ., Diss., 2009

Inköp är idag av central betydelse för ett företags lönsamhet och bidrar även på ett avgörande sätt till dess konkurrenskraft. Vidare ökar vikten av effektivt inköp av indirekt material i takt med den ökande andelen outsourcing av icke-kärnkompetenser, expansion av servicesektorn och en ökande global konkurrens. Kategoristyrning är idag en grundläggande del av en professionell inköpsorganisation och innefattar en metodik för indelning av företagets strategiska inköpsutgifter i kategorier och segment. Framtagningen av en kategoristruktur inleder kategoristyrningsarbetet och kan sägas vara grunden till utförandet av kategoristyrning. Studiens syfte har varit att undersöka hur en kategoristruktur för strategiskt inköp av indirekt material kan utformas med hjälp av metodiken för kategoristyrning. Studien är genomförd inom tillverkningsindustrin och har utförts som en fallstudie vid Väderstad AB:s strategiska inköpsavdelning för indirekt material. Företagets nuvarande kategoristruktur var utformad empiriskt med tiden och saknade en genomtänkt grundprincip för vilka inköp som skulle inkluderas. Därmed behövdes strukturen göras om samt anpassas till företagets ambitioner om att inleda kategoristyrningsarbete inom indirekt material. Studien innefattar även en nulägesanalys av företagets förutsättningar för kategoristyrning utifrån identifierade förutsättningar i litteraturen. För att uppfylla syftet har primärt historiska inköpsutgifter från företagets affärssystem använts tillsammans med intervjuer och inköpsutgiftsinformation. Därefter har litteraturens metodik kring kategorisering använts för att skapa kategorier och segment. Studiens huvudsakliga resultat är den framtagna kategoristrukturen bestående av 22 kategorier. Kategoristrukturen är utifrån paretoprincipen baserad på 20 % av antalet aktiva leverantörer vars summerade inköpsutgifter täcker 93 % av inköpsutgifterna för indirekt material. Studien resulterar även i en identifiering av indirekta inköp som ej tidigare styrts via den strategiska inköpsavdelningen. Utifrån nulägesanalysen av företagets förutsättningar för kategoristyrning, har studien även tagit fram rekommendationer för hur förutsättningarna kan säkerställas. Implementeringen av strukturen bör göras efter det att förutsättningarna säkerställts. Införs studiens framtagna kategoristruktur kan större fokus läggas på de inköpsbehov som är av strategisk betydelse utifrån summerade inköpsutgifter.

Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff Spaces are the algebras of the codensity monad induced by the inclusion of finite sets in the category of sets. Similarly linearly compact vector spaces are the algebras of the codensity monad induced by the inclusion of finite dimensional vector spaces in the category of vector spaces. So in these two examples the notions of finiteness, compactness and codensity are intertwined. In this thesis we generalise these results. To do this we generalise the notion of ultrafilter, and follow the intuition of the compact Hausdorff case. We give definitions of general notions of "finiteness" and "compactness" and show that the algebras for the codensity monad induced by the "finite" objects are exactly the "compact" objects.

The thesis shows the approaches of cognitive grammar to the description and analysis of case category's functioning in Czech and Russian languages. Attention is limited to the cognitive grammar as it interpreted by American linguist R. Langacker. Cognitive researches on Slavic languages by L. Janda are also crucial for this diploma. From this point of view the thesis's author studies the interferential phenomena which are typical for Russian-language speakers when they use the Czech language. In other words, by means of conceptual apparatus relevant to cognitive grammar author explains the different use of case category in both these languages. Keywords Cognitive grammar, case, interference, Czech language, Russian language

Part I of this thesis concerns the question in which dimensions manifolds with higher orientability properties can have an odd Euler characteristic. In chapter 1 I prove that a k-orientable manifold (or more generally Poincare complex) has even Euler characteristic unless the dimension is a multiple of 2^k+1, where we call a manifold k-orientable if the i^th Stiefel-Whitney class vanishes for all 0 < i < 2^k (k ≥ 0). For k = 0, 1, 2, 3, k-orientable manifolds with odd Euler characteristic exist in all dimensions 2^k+1m, but whether there exist a 4-orientable manifold with an odd Euler characteristic is an open problem. In Chapter 2 I present calculations on the cohomology of the first two Rosenfeld planes, revealing that (O ⊗ C)P² is 2-orientable and (O ⊗ H)P² is at least 3-orientable. Part II discusses the homotopy type of spaces of nested manifolds. I prove that the space of d-dimensional manifolds with k-dimensional submanifolds inside Rⁿ has the homotopy type of a linearised model T_k<d, which can be thought of as a space of off-set d-planes inside Rⁿ with a (potentially empty) off-set k-plane inside of it, compactified with a point at infinity representing the empty set. Applying an induction I generalise this result to the case of higher nestings, establishing that the space Ψ_I (Rⁿ) of nested manifolds inside Rⁿ, for I a finite list of strictly increasing dimensions between 0 and n - 1, has the homotopy type of a linearised model space T_I.

The research on bilingual language processing explores two main avenues of relevance to the present study: lexico-semantic access and cognitive control. Lexico-semantic access research investigates the manner in which bilingual individuals retrieve single words from their lexical system. Healthy bilingual individuals can manipulate their lexico-semantic access to accommodate settings in which code- or language-switching is expected. Alternatively, they can manipulate their lexico-semantic access to speak only their first (L1) or second (L2) languages. Cognitive control, also known as executive functioning, is closely related to lexico-semantic access. Specifically, bilingual individuals maintain and switch between their languages through a mechanism known as cognitive control. Both cognitive control and lexico-semantic access are important for language processing in healthy bilingual individuals as well as bilingual persons with aphasia (BPWA). However, the extent to which BPWA utilize each of these processes in the production of single words is still unknown. The present study used a method of verbal fluency in the form of a novel modified category generation task to assess the relative contributions of lexico-semantic access and cognitive control in bilingual healthy controls and BPWA.

In this thesis, tools of categorical quantum mechanics are used to explain natural language from a cognitive point of view. Categories of generalized relations are developed for the task, examples are provided, and languages that are particularly tricky to describe using this approach are taken into consideration.

The main goal of this thesis is to construct a tensor product on the 2-category BFC-A of braided fusion categories containing a symmetric fusion category A. We achieve this by introducing the new notion of Z(A)-crossed braided categories. These are categories enriched over the Drinfeld centre Z(A) of the symmetric fusion category. We show that Z(A) admits an additional symmetric tensor structure, which makes it into a 2-fold monoidal category. ByTannaka duality, A= Rep(G) (or Rep(G; w)) for a finite group G (or finite super-group (G,w)). Under this identication Z(A) = VectG[G], the category of G-equivariant vector bundles over G, and we show that the symmetric tensor product corresponds to (a super version of) to the brewise tensor product. We use the additional symmetric tensor product on Z(A) to define the composition in Z(A)-crossed braided categories, whereas the usual tensor product is used for the monoidal structure. We further require this monoidal structure to be braided for the switch map that uses the braiding in Z(A). We show that the 2-category Z(A)-XBF is equivalent to both BFC=A and the 2-category of (super)-G-crossed braided categories. Using the former equivalence, the reduced tensor product on BFC-A is dened in terms of the enriched Cartesian product of Z(A)-enriched categories on Z(A)-XBF. The reduced tensor product obtained in this way has as unit Z(A). It induces a pairing between minimal modular extensions of categories having A as their Mueger centre.