Infinite loop spaces,and coherence for symmetric monoidal bicategories |
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Authors: | Nick Gurski Angélica M Osorno |
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Institution: | 1. School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, UK;2. Department of Mathematics, University of Chicago, Chicago, IL 60637, USA |
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Abstract: | This paper proves three different coherence theorems for symmetric monoidal bicategories. First, we show that in a free symmetric monoidal bicategory every diagram of 2-cells commutes. Second, we show that this implies that the free symmetric monoidal bicategory on one object is equivalent, as a symmetric monoidal bicategory, to the discrete symmetric monoidal bicategory given by the disjoint union of the symmetric groups. Third, we show that every symmetric monoidal bicategory is equivalent to a strict one. |
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Keywords: | Symmetric monoidal bicategory Coherence E&infin space |
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