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Transactions of the American Mathematical Society

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Braided injections and double loop spaces


Authors: Christian Schlichtkrull and Mirjam Solberg
Journal: Trans. Amer. Math. Soc. 368 (2016), 7305-7338
MSC (2010): Primary 18D10, 18D50, 55P48; Secondary 55P43
DOI: https://doi.org/10.1090/tran/6614
Published electronically: November 16, 2015
MathSciNet review: 3471092
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Abstract: We consider a framework for representing double loop spaces (and more generally $ E_2$ spaces) as commutative monoids. There are analogous commutative rectifications of braided monoidal structures and we use this framework to define iterated double deloopings. We also consider commutative rectifications of $ E_{\infty }$ spaces and symmetric monoidal categories and we relate this to the category of symmetric spectra.


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Additional Information

Christian Schlichtkrull
Affiliation: Department of Mathematics, University of Bergen, P.O. Box 7800, N-5020 Bergen, Norway
Email: christian.schlichtkrull@math.uib.no

Mirjam Solberg
Affiliation: Department of Mathematics, University of Bergen, P.O. Box 7800, N-5020 Bergen, Norway
Email: mirjam.solberg@math.uib.no

DOI: https://doi.org/10.1090/tran/6614
Keywords: Braided monoidal categories, double loop spaces, diagram spaces
Received by editor(s): March 5, 2014
Received by editor(s) in revised form: September 29, 2014
Published electronically: November 16, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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