کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665984 1633840 2013 67 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homotopy colimits of algebras over Cat-operads and iterated loop spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Homotopy colimits of algebras over Cat-operads and iterated loop spaces
چکیده انگلیسی
We extend Thomasonʼs homotopy colimit construction in the category of permutative categories to categories of algebras over an arbitrary Σ-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 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 Thomasonʼs corresponding result about infinite loop spaces and obtain related results about braided monoidal categories and 2-fold loop spaces.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 248, 25 November 2013, Pages 1089-1155
نویسندگان
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