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Homotopy coherent centers versus centers of homotopy categories. http://arxiv.org/abs/1305.3029 William G. Dwyer Department of Mathematics University of Notre Dame Notre Dame
 IN 46556 USA dwyer.1@nd.edu Markus Szymik Department of Mathematical Sciences NTNU Norwegian University of Science and Technology 7491 Trondheim NORWAY markus.szymik@math.ntnu.no
"... Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as Hochschild cohomology type invariants in contexts that are no ..."
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Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as Hochschild cohomology type invariants in contexts that are not necessarily linear or stable, and we argue that they are more appropriate to higher categorical contexts than the centers of their homotopy or derived categories. Among many other things, we present an obstruction theory for realizing elements in the centers of homotopy categories, and a BousfieldKan type spectral sequence that computes the homotopy groups. Nontrivial classes of examples are given as illustration throughout. MSC: primary 18G50, 55U40, secondary 16E40, 18G40, 55S35
Tannaka duality for enhanced triangulated categories, ArXiv eprints
, 2013
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PROFINITE GSPECTRA
 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 LubinTate spectra under the action of the extended Morava stabilizer group.
JOURNAL OF PURE AND APPLIED ALGEBRA Comparison of the geometric bar and Wconstructions
, 1995
"... Dedicated to the memory of V.K.A.M. Gugenheim For a simplicial group K, the realization of the Wconstruction 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 Wconstruc ..."
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Dedicated to the memory of V.K.A.M. Gugenheim For a simplicial group K, the realization of the Wconstruction 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 Wconstruction 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
DSTRUCTURES AND DERIVED KOSZUL DUALITY FOR UNITAL OPERAD ALGEBRAS
"... Abstract. Generalizing a concept of Lipshitz, Ozsváth and Thurston from Bordered Floer homology, we define Dstructures on algebras of unital operads. This construction gives rise to an equivalence of derived categories, which can be thought of as a unital version of Koszul duality using nonunital ..."
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Abstract. Generalizing a concept of Lipshitz, Ozsváth and Thurston from Bordered Floer homology, we define Dstructures on algebras of unital operads. This construction gives rise to an equivalence of derived categories, which can be thought of as a unital version of Koszul duality using nonunital Quillen homology, even though the nonunital Quillen homology of unital objects is zero. 1.
(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.
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
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"... Closed model categories for presheaves of simplicial groupoids and presheaves of 2groupoids by Zhiming Luo ..."
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Closed model categories for presheaves of simplicial groupoids and presheaves of 2groupoids by Zhiming Luo
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 2type. 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 2type. 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.