Algebraic theories and algebraic categories offer an innovative and revelatory description of the syntax and the semantics. An algebraic theory is a concrete mathematical object -- the concept -- namely a set of variables together with formal symbols and equalities between these terms; stated otherwise, an algebraic theory is a small category with finite products. An algebra or model of the theory is a set-theoretical interpretation -- a possible meaning -- or, more categorically, a finite product-preserving functor from the theory into the category of sets. We call the category of models of an algebraic theory an algebraic category. By generalising the theory we do generalise the models. This concept is the fascinating aspect of the subject and the reference point of our project. We are interested in the study of categories of models. We pursue our task by considering models of different theories and by investigating the corresponding categories of models they constitute. We analyse localizations (namely, fully faithful right adjoint functors whose left adjoint preserves finite limits) of algebraic categories and localizations of presheaf categories. These are still categories of models of the corresponding theory. We provide a classification of localizations and a classification of geometric morphisms (namely, functors together with a finite limit-preserving left adjoint), in both the presheaf and the algebraic context.

We define morphism (E, M)-structures in an abstract category, develop their basic properties and present some examples. We also consider the existence of such factorization structures, and find conditions under which they can be extended to factorization structures for certain classes of sources. There is a Galois correspondence between the collection of all subclasses of X-morphisms and the collection of all subclasses of X-objects. A-epimorphisms diagonalize over A-regular morphisms. Given an (E, M)-factorization structure on a finitely complete category, E-separated objects are those for which diagonal morphisms lie in M. Other characterizations of E-separated objects are given. We give a bijective correspondence between the class of all (E, M)factorization structures with M contained in the class of all X-embeddings and the class of all strong limit operators. We study M-preserving morphisms, M-perfect morphisms and M-compact objects in a morphism (E, M)-hereditary construct, and prove some of their properties which are analogous to the topological ones. / Mathematical Sciences / M. Sc. (Mathematics)

No description available.

We develop some basic homological theory of hopfological algebra as defined by Khovanov. A simplicial bar resolution for an arbitrary hopfological module is constructed, and some derived analogue of Morita theory is established. We also discuss about some special classes of examples that appear naturally in categorification.

This dissertation explores the drivers of why organizations, as members of its market category, choose to conform or deviate from the category’s codes. In essence, codes are the social rules category members are expected to abide by and that underpin the very existence of a category. Given the importance of producer conformity in upholding a category’s continued existence, code deviance then seems a counterintuitive strategy to pursue. Nonetheless, organizations are known to defy codes in certain instances, sometimes even pairing the violation simultaneously with conformity to other codes. On top of this, organizations also seem to be able to strategically decide which codes they will abide by to a certain extent. Each of the three papers in this dissertation investigates why organizations may choose to either conform or deviate by, respectively, examining (1) the identity difference between the code violator with the potential adopter of the code violation, (2) the taken-for-grantedness of the category the organization is a part of, and (3) the individual status and organizational identity (insider-outsider) of the producer. The main overarching finding of this dissertation is that organizations will take into account both its internal resources and external socio-environment to decide which strategy it will deploy and whether it can afford to do so. All in all, this dissertation specifies how the three factors mentioned may affect an organization’s propensity to conform or violate to category codes.

The compact symmetric multicategories (CSMs) introduced by Joyal and Kock in their 2011 note 'Feynman Graphs, and Nerve Theorem for Compact Symmetric Multicategories' [JK11] directly generalise a number of unital operad types, such as wheeled properads, that admit a contraction operation as well as an operadic multiplication. These structures are known to exhibit strange behaviour related to the contraction of units, and this is problematic for [JK11]. In this thesis, I modify the construction of [JK11] to obtain non unital (coloured) modular operads as algebras for a monad defined in terms of connected graphs, and use this as a foundation for a new construction of CSMs based on special graph morphisms. A corresponding nerve theorem characterises CSMs in terms of a Segal condition. This construction sheds light, and provides some control, on the behaviour of the contracted units.

This thesis investigates the functional categories in the vP domain, including aspect, modality, and focus. For this research initiative, five constructions were examined: the Mandarin temporal adverbial, the Mandarin excessive ta, the Mandarin de/bu, the Turkish question particle –mI, and the Armenian auxiliary constructions. These constructions involve functional categories that are expected to appear at the C/IP periphery; however, they surface inside the vP domain. The existence of these low grammatical elements raises non-trivial questions such as how functional categories should be mapped out in the structure, and whether a unified structure can be proposed to account for the cross-linguistic phenomena examined in this thesis. The investigation of these constructions showed that there are cross-domain interactions between low and high functional categories. While Mandarin temporal adverbial constructions showed interactions between viewpoint aspect and lexical aspect via the distributions of the temporal adverbials and various co-occurrence restrictions, the other four constructions demonstrated interactions between the low and the high categories via intervention effects. I argue that low functional categories must be licensed by their counterparts in the C/IP domain, and that the licensing relation and the structural conditions imposed on this relation can be captured if an Agree relation is established between the functional categories in these two domains. The analysis also reveals that low functional categories are the result of feature lowering from v* to some functional projection below it, and the formal features of the low functional categories must assign their values to their counterparts in the C/IP domain via Agree to provide a meaningful input to LF. I propose a parallel analysis between CP and vP to account for the existence of the low grammatical elements in two respects: (1) C and *v, as phase heads, have an edge feature (EPP) and Agree features that need to be valued and/or checked at a functional projection lower than the each phase head; (2) the formal features of C can appear at *v if they are licensed by an associate feature present in the C/T domain for the purpose of Full Interpretation (Chomsky 1995, 2000).

No description available.

Today’s students are struggling to achieve a pass level at secondary education and have difficulties in learning core subjects such as English. By increasing the size of classes, reducing the number of teachers and constantly reviewing the curriculum, the students are finding it more difficult to achieve a pass grade in foreign languages. Therefore, the aim of the present study is to acquire a broader knowledge of how, and whether, Earl W Stevick’s seven learning categories are applied in Swedish education. The findings of this study indicated that some of the secondary school teachers provide occasionally for all different learning categories, but were unable to accommodate all styles regularly. Moreover, university lecturers were unfamiliar with Stevick’s learning categories. Thus, his theories were not part of the formal university curriculum. However, as only one secondary school and seven universities were included in the study, no generalization for the Swedish educational system could be made, and a more extensive research study is encouraged.

Classical and quantum Chern-Simons with gauge group U(1)N were classified by Belov and Moore in [BM05]. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence is well known between ordinary (2 + 1)-dimensional TQFTs and modular tensor categories. We study group categories and extend them slightly to produce modular tensor categories that correspond to toral Chern-Simons. Group categories have been widely studied in other contexts in the literature [FK93],[Qui99],[JS93],[ENO05],[DGNO07]. The main result is a proof that the associated projective representation of the mapping class group is isomorphic to the one from toral Chern-Simons. We also remark on an algebraic theorem of Nikulin that is used in this paper. / text