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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Bourke, J., Gurski, N. The Gray Tensor Product Via Factorisation. Appl Categor Struct 25, 603–624 (2017). https://doi.org/10.1007/s10485-016-9467-6
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DOI: https://doi.org/10.1007/s10485-016-9467-6