Bourke, J.D. and Gurski, M.N. (2016) The Gray tensor product via factorisation. Applied Categorical Structures. ISSN 0927-2852
Abstract
We discuss the folklore construction of the Gray tensor product of 2-categories as obtained by factoring the map from the funny tensor product to the cartesian product. We show that this factorisation can be obtained without using a concrete presentation of the Gray tensor product, but merely its defining universal property, and use it to give another proof that the Gray tensor product forms part of a symmetric monoidal structure. The main technical tool is a method of producing new algebra structures over Lawvere 2-theories from old ones via a factorisation system.
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Copyright, Publisher and Additional Information: | © 2016 Springer. This is an author produced version of a paper subsequently published in Applied Categorical Structures. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | monoidal category; factorisation system; Lawvere theory | ||||
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) | ||||
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 15 Sep 2016 13:25 | ||||
Last Modified: | 08 Oct 2017 18:19 | ||||
Published Version: | https://dx.doi.org/10.1007/s10485-016-9467-6 | ||||
Status: | Published | ||||
Publisher: | Springer Verlag (Germany) | ||||
Identification Number: | https://doi.org/10.1007/s10485-016-9467-6 |