Geometry and Topology Seminar (Math) - Alexander Campbell

Speaker: Alexander Campbell (Macquarie University)

"A model-independent construction of the Gray monoidal structure for (∞,2)(∞,2)-categories"

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)(∞,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)(∞,2)-categories, and explain how our results can be used to simplify (though not yet solve) one of these problems.

https://researchers.mq.edu.au/en/persons/alexander-campbell