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Rectification of weak
product algebras over an operad in $\mathcal{C}\mathit{at}$
and $\mathcal{T}\mathit{op}$ and applications
Zbigniew Fiedorowicz, Manfred Stelzer and Rainer M Vogt |
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Algebraic & Geometric Topology 16 (2016) 711–755
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Abstract |
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We develop an alternative to the May–Thomason construction used to compare operad-based infinite loop machines to those of Segal, which rely on weak products. Our construction has the advantage that it can be carried out in , whereas their construction gives rise to simplicial categories. As an application we show that a simplicial algebra over a –free operad is functorially weakly equivalent to a algebra over . When combined with the results of a previous paper, this allows us to conclude that, up to weak equivalences, the category of –categories is equivalent to the category of –spaces, where is the classifying space functor. In particular, –fold loop spaces (and more generally spaces) are functorially weakly equivalent to classifying spaces of –fold monoidal categories. Another application is a change of operads construction within . |
Keywords
operads, categories, loop space machines
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Mathematical Subject Classification 2010
Primary: 18D50
Secondary: 55P48
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References |
Publication
Received: 23 May 2014
Revised: 3 June 2015
Accepted: 23 June 2015
Published: 26 April 2016
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Authors |
| Zbigniew Fiedorowicz | |
| Department of Mathematics The Ohio State University 100 Mathematics Building 231 West 18th Avenue Columbus, OH 43210-1174 USA |
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| http://https://people.math.osu.edu/fiedorowicz.1/ | |
| Manfred Stelzer | |
| Fachbereich
Mathematik/Informatik Universität Osnabrück Albrechtstrasse 28a D-49076 Osnabrück Germany |
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| Rainer M Vogt | |
| Fachbereich
Mathematik/Informatik Universität Osnabrück Albrechtstrasse 28a D-49069 Osnabrück Germany |
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