2011/09/01 by Zbigniew Fiedorowicz, Fiedorowicz, Zbigniew, Manfred Stelzer +3
Mathematics · #18C20 #18D10 #18D50 #55P35 #55P47 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1109.0265
openalex publication_date 2011/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Cn-spaces after formally inverting certain classes of weak equivalences, where Cn 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.