The Gray tensor product via factorisation

John Bourke*, Nick Gurski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)603–624
Number of pages22
JournalApplied Categorical Structures
Issue number4
Early online date7 Oct 2016
Publication statusPublished - Aug 2017
Externally publishedYes


  • Monoidal category
  • Factorisation system
  • Lawvere theory


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