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Morita theory in abelian, derived and stable model categories, Structured ring spectra
 London Math. Soc. Lecture Note Ser
, 2004
"... These notes are based on lectures given at the Workshop on Structured ring spectra and ..."
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These notes are based on lectures given at the Workshop on Structured ring spectra and
Homotopy theory of spectral categories
, 2008
"... Abstract. We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories. Following Toën’s work on DG categories, we describe the mapping space between two spectral categories A ..."
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Cited by 5 (1 self)
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Abstract. We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories. Following Toën’s work on DG categories, we describe the mapping space between two spectral categories A and B in terms of the nerve of a certain category of ABbimodules, and show that the homotopy category of spectral categories obtained admits internal Hom’s relative to the derived smash product. As an application, we obtain a simple conceptual characterization of topological
Cohomology theories for highly structured ring spectra. arXiv: math.AT/0211275
"... Abstract. This is a survey paper on cohomology theories for A ∞ and E ∞ ring spectra. Different constructions and main properties of topological AndréQuillen cohomology and of topological derivations are described. We give sample calculations of these cohomology theories and outline applications to ..."
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Abstract. This is a survey paper on cohomology theories for A ∞ and E ∞ ring spectra. Different constructions and main properties of topological AndréQuillen cohomology and of topological derivations are described. We give sample calculations of these cohomology theories and outline applications to the existence of A ∞ and E ∞ structures on various spectra. We also explain the relationship between topological derivations, spaces of multiplicative maps and moduli spaces of multiplicative structures. 1.
RIGIDITY THEOREMS IN STABLE HOMOTOPY THEORY CASE FOR SUPPORT
"... He spent 11 years in a succession of postdoctoral positions in Canada, USA and Britain, including two years at the University of Chicago as an L. E. Dickson Instructor and 2 years as an EPSRC Advanced Fellow, before being appointed in 1991 to a Lectureship (and subsequently in 1996 to a Readership) ..."
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He spent 11 years in a succession of postdoctoral positions in Canada, USA and Britain, including two years at the University of Chicago as an L. E. Dickson Instructor and 2 years as an EPSRC Advanced Fellow, before being appointed in 1991 to a Lectureship (and subsequently in 1996 to a Readership) at the University of Glasgow. His research has centred on algebraic topology, especially stable homotopy theory. In particular he has focused on applications of algebra and number theory to complex oriented and periodic cohomology theories (especially Ktheory and elliptic cohomology). For a representative overview of his work see [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. In recent years he has been very involved in work on structured ring spectra and related topics, and organised a series of workshops in Glasgow, Bonn and Rosendal (Norway), as well as editing a book based on the first of these [13]. Sarah Whitehouse was awarded a Ph.D. from the University of Warwick in 1994. She spent several years in France, as a MarieCurie postdoctoral researcher at the Université ParisNord and as a Lecturer at the Université d’Artois. She joined the University of Sheffield as a Lecturer in 2002 and was promoted to Senior Lecturer in 2005. Much of her work has involved the algebras of operations or cooperations of generalised cohomology theories [18, 19, 27, 38]. Recently, this has given new results for complex Ktheory, cobordism and the Morava Ktheories