The main purpose of this work is to study model category structures (in the sense of Quillen) on the categories of small categories and small symmetric multicategories enriched over an arbitrary monoidal model category. Among these model structures, there is one of the greatest importance in applications. We call it the Dwyer-Kan model structure (for enriched categories or enriched symmetric multicategories), and a large amount of this work is dedicated to establishing it for different choices of monoidal model categories. Another model structure that we study is what we call the fibred model structure, again for both small categories and small symmetric multicategories enriched over a suitable monoidal model category. / The other purpose of this work is to study model category structures on the category of comonoids in a monoidal model category.

This thesis studies the pre-quantization of quasi-Hamiltonian group actions from a cohomological viewpoint. The compatibility of pre-quantization with symplectic reduction and the fusion product are established, and are used to understand the necessary and sufficient conditions for the pre-quantization of M(G,S), the moduli space of at flat G-bundles over a closed surface S. For a simply connected, compact, simple Lie group G, M(G,S) is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this thesis determines the obstruction, namely a certain 3-dimensional cohomology class, that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G. Partial results are obtained for the case of a surface S with marked points. Also, it is shown that via the bijective correspondence between quasi-Hamiltonian group actions and Hamiltonian loop group actions, the corresponding notions of prequantization coincide.

Thesis (Ph. D.)--Oregon State University, 1990. / Typescript (photocopy). Includes bibliography (leaves 65-67). Also available on the World Wide Web.

Thesis (Ph. D.)--Michigan State University. Dept. of Mathematics, 2008. / Title from PDF t.p. (viewed Aug. 17, 2009). Includes bibliographical references (p. 84-87). Also issued in print.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1997. / Includes bibliographical references (p. 72-74).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Let Mk be the category of algebras over a unique factorization domain k, and let ind-Affk denote the category of pro-representable functors from Mk to the category E of sets. It is shown that ind-Affk is a closed model category in such a way that its associated homotopy category Ho(ind-Affk) is equivalent to the homotopy category Ho(S) which comes from the category S of simplicial sets. The equivalence is induced by functors Sk: ind-Affk -> S and Rk: S-> ind-Affk. In an effort to determine what is measured by the homotopy groups πi(X) := πi. (Sk X) of X in ind-Affk in the case where k is an algebraically closed field, some homotopy groups of affine reduced algebraic groups G over k are computed. It is shown that, if G is connected, then π₀ (G) = * if and only if the group G(k) of k-rational points of G is generated by unipotents. A fibration theory is developed for homomorphisms of algebraic groups which are surjective on rational points which allows the computation of the homotopy groups of any connected algebraic group G in terms of the homotopy groups of the universal covering groups of the simple algebraic subgroups of the associated semi-simple group G/R(G), where R(G) is the solvable radical of G. The homotopy groups of simple Chevalley groups over almost all fields k are studied. It is shown that the homotopy groups of the special linear groups S1n and of the symplectic groups Sp2m converge, respectively, to the K-theory and ₋₁L-theory of the underlying field k. It is shown that there are isomorphisms π₁ (S1n ) = H₂(S1n (k);Z) = K₂(k) for n ≥ 3 and almost all fields k, and π₁ (Sp₂m ) = H₂(Sp₂m) (k);Z) = ₋₁L₂(k) for m ≥ 1 and almost all fields k of characteristic ≠ 2, where Z denotes the ring of integers. It is also shown that π₁(Sp₂m) = H₂(Sp2m(k);Z) = K₂ (k) if k is algebraically closed of arbitrary characteristic. A spectral sequence for the homology of the classifying space of a simplicial group is used for all of these calculations. / Science, Faculty of / Mathematics, Department of / Graduate

No description available.

We investigate quotient-fine nearness frames, showing that they are reflective in the category of strong nearness frames, and that, in those with spatial completion, any near subset is contained in a near grill. We construct two categories, each of which is shown to be equivalent to that of quotient-fine nearness frames. We also consider some subcategories of the category of nearness frames, which are co-hereditary and closed under coproducts. We give due attention to relations between these subcategories. We introduce totally strong nearness frames, whose category we show to be closed under completions. We investigate N-homomorphisms and remote points in the context of totally bounded uniform frames, showing the role played by these uniform N-homomorphisms in the transfer of remote points, and their relationship with C -quotient maps. A further study on grills enables us to establish, among other things, that grills are precisely unions of prime filters. We conclude the thesis by showing that the lattice of all nearnesses on a regular frame is a pseudo-frame, by which we mean a poset pretty much like a frame except for the possible absence of the bottom element. / Mathematical Sciences / Ph.D. (Mathematics)

Chan, Kam Fung. / "September 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Main result --- p.6 / Chapter 1.2 --- Useful definition --- p.7 / Chapter 1.3 --- Outline of proof of Theoreml.l --- p.11 / Chapter 2 --- Proof of Theorem1.2 and 13 --- p.12 / Chapter 2.1 --- The spaces \hV\ and \hW\ --- p.13 / Chapter 2.2 --- The space \hWloc\ --- p.19 / Chapter 2.3 --- The space \Wloc\ --- p.23 / Chapter 3 --- Proof of Theoreml4 --- p.26 / Chapter 3.1 --- Sheaves with category structure --- p.26 / Chapter 3.2 --- W° and hW° --- p.29 / Chapter 3.3 --- Armlets --- p.29 / Chapter 4 --- Proof of Theorem15 --- p.36 / Chapter 4.1 --- Homotopy colimit decompositions --- p.36 / Chapter 4.2 --- Introducing boundaries --- p.50 / Chapter 4.2.1 --- Proof of Theorem4.21 --- p.53 / Chapter 4.2.2 --- Proof of Lemma4.20 --- p.56 / Chapter 4.3 --- Using the Harer-Ivanov stabilization theorem --- p.58 / Bibliography --- p.61