Homotopy colimits of algebras over Cat-operads and iterated loop spaces

Autor(en): Fiedorowicz, Z.
Stelzer, M. 
Vogt, R. M.
Stichwörter: Braided monoidal categories; Homotopy colimit; INFINITY; Iterated loop spaces; Iterated monoidal categories; K-THEORY; LIMITS; Mathematics; MODEL CATEGORIES; MONOIDS; Operads; Symmetric monoidal categories; TOPOLOGICAL-SPACES
Erscheinungsdatum: 2013
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN MATHEMATICS
Volumen: 248
Startseite: 1089
Seitenende: 1155
Zusammenfassung: 
We extend Thomason's homotopy colimit construction in the category of permutative categories to categories of algebras over an arbitrary Sigma-free Cat-operad and analyze its properties. We then use this homotopy colimit to prove that the classifying space functor induces an equivalence between the category of n-fold monoidal categories and the category of C-n-spaces after formally inverting certain classes of weak equivalences, where C-n is the little n-cubes operad. As a consequence we obtain an equivalence of the categories of n-fold monoidal categories and the category of n-fold loop spaces and loop maps after localization with respect to some other class of weak equivalences. We recover Thomason's corresponding result about infinite loop spaces and obtain related results about braided monoidal categories and 2-fold loop spaces. (C) 2013 Elsevier Inc. All rights reserved.
ISSN: 00018708
DOI: 10.1016/j.aim.2013.07.016

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