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March 17, 2021
Wednesday, March 17
Geometry and Topology
Time: 19:00
Speaker: Alexander Campbell (Macquarie University)
Title: "A model-independent construction of the Gray monoidal structure for (,2)-categories"
Room: Zoom Meeting ID: 958 6908 4555

Abstract: In this talk I will describe joint work with Yuki Maehara in which we give a model-independent (i.e. a purely -categorical) construction of the (non-symmetric) Gray monoidal structure on the -category of (,2)-categories. Our construction is a generalisation to the -categorical setting of a construction of the Gray monoidal structure for 2-categories due to Ross Street, which uses the techniques from Brian Day's PhD thesis for extending a monoidal structure along a dense functor. The proof of our construction uses, among other things, the results from Yuki's PhD thesis on the Gray tensor product for 2-quasi-categories. I will also mention a few of the open problems concerning the Gray monoidal structure for (,2)-categories, and explain how our results can be used to simplify (though not yet solve) one of these problems.