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**11 - 20**of**20**### JOURNAL OF PURE AND APPLIED ALGEBRA Comparison of the geometric bar and W-constructions

, 1995

"... Dedicated to the memory of V.K.A.M. Gugenheim For a simplicial group K, the realization of the W-construction WK + WK of K is shown to be naturally homeomorphic to the universal bundle E]K]--t BIK of its geometric realization]Kl. The argument involves certain recursive descriptions of the W-construc ..."

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Dedicated to the memory of V.K.A.M. Gugenheim For a simplicial group K, the realization of the W-construction WK + WK of K is shown to be naturally homeomorphic to the universal bundle E]K]--t BIK of its geometric realization]Kl. The argument involves certain recursive descriptions of the W-construction and classifying bundle and relies on the facts that the realization functor carries an action of a simplicial group to a geometric action of its realization and preserves reduced cones and colimits. @ 1998 Elsevier Science B.V. All rights reserved. AMS Cluss$ccrrior~: 55405; 55P35; I8G30

### unknown title

"... Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids by Zhi-ming Luo ..."

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Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids by Zhi-ming Luo

### School of Mathematics,

, 2008

"... We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial ..."

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We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial

### unknown title

"... Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids by Zhi-Ming Luo ..."

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Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids by Zhi-Ming Luo

### S-categories, S-groupoids, Segal categories and quasicategories

, 2008

"... The notes were prepared for a series of talks that I gave in Hagen in late June and early July 2003, and, with some changes, in the University of La Laguña, the Canary Islands, in September, 2003. They assume the audience knows some abstract homotopy theory and as Heiner Kamps was in the audience in ..."

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The notes were prepared for a series of talks that I gave in Hagen in late June and early July 2003, and, with some changes, in the University of La Laguña, the Canary Islands, in September, 2003. They assume the audience knows some abstract homotopy theory and as Heiner Kamps was in the audience in Hagen, it is safe to assume that the notes assume a reasonable knowledge of our book, [26], or any equivalent text if one can be found! What do the notes set out to do? “Aims and Objectives! ” or should it be “Learning Outcomes”? • To revisit some oldish material on abstract homotopy and simplicially enriched categories, that seems to be being used in today’s resurgence of interest in the area and to try to view it in a new light, or perhaps from new directions; • To introduce Segal categories and various other tools used by the Nice-Toulouse group of abstract homotopy theorists and link them into some of the older ideas; • To introduce Joyal’s quasicategories, (previously called weak Kan complexes but I agree with André that his nomenclature is better so will adopt it) and show how that theory links in with some old ideas of Boardman and Vogt, Dwyer and Kan, and Cordier and myself; • To ask lots of questions of myself and of the reader. The notes include some material from the ‘Cubo ’ article, [35], which was itself based on notes for a course at the Corso estivo Categorie e Topologia in 1991, but the overlap has been kept as small as is feasible as the purpose and the audience of the two sets of notes are different and the abstract homotopy theory has ‘moved on’, in part, to try the new methods out on those same ‘old ’ problems and to attack new ones as well. As usual when you try to specify ‘learning outcomes ’ you end up asking who has done the learning, the audience? Perhaps. The lecturer, most certainly! 1

### Contemporary Mathematics Formal Homotopy Quantum Field Theories, II: Simplicial Formal Maps

, 2005

"... Abstract. Simplicial formal maps were introduced in the first paper of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a natural generalisation can handle much more general backgrounds. The questi ..."

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Abstract. Simplicial formal maps were introduced in the first paper of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a natural generalisation can handle much more general backgrounds. The question of the geometric interpretation of these formal maps is partially answered in terms of combinatorial bundles. This suggests new interpretations of HQFTs.

### (PhD supervisor) Acknowledgements

"... This thesis is my own work, except where stated in the text, and has not been submitted for any other degree in this or any other institution. ..."

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This thesis is my own work, except where stated in the text, and has not been submitted for any other degree in this or any other institution.

### PROFINITE G-SPECTRA

- HOMOLOGY, HOMOTOPY AND APPLICATIONS, VOL. 15(1), 2013, PP.151–189
, 2013

"... We construct a stable model structure on profinite spectra with a continuous action of an arbitrary profinite group. The motivation is to provide a natural framework in a subsequent paper for a new and conceptually simplified construction of continuous homotopy fixed point spectra and of continuous ..."

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We construct a stable model structure on profinite spectra with a continuous action of an arbitrary profinite group. The motivation is to provide a natural framework in a subsequent paper for a new and conceptually simplified construction of continuous homotopy fixed point spectra and of continuous homotopy fixed point spectral sequences for Lubin-Tate spectra under the action of the extended Morava stabilizer group.