Homotopy Colimits of Algebras Over Cat-Operads and Iterated Loop Spaces

Autor:	Fiedorowicz, Zbigniew, Stelzer, Manfred, Vogt, Rainer M.
Rok vydání:	2011
Předmět:	Mathematics - Algebraic Topology 55P35 55P47 55P48 18D10 18D50 18C20
Druh dokumentu:	Working Paper
Popis:	We extend Thomason's homotopy colimit construction in the category of permutative categories to categories of algebras over an arbitrary $\Cat$ 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 $\mathcal{C}_n$-spaces after formally inverting certain classes of weak equivalences, where $\mathcal{C}_n$ 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. Comment: 78 pages. This version corrects a small error in the previous revision
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1109.0265 Zobrazit plný text záznamu View this record from Arxiv