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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
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 |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/K007343/1 |
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: | 10.1007/s10485-016-9467-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104612 |