Monoidal centres and groupoid-graded categories

Ross Street – 22 June 2022

(joint work with Branko Nikoli\'c) The paper on which my 1 July 2020 talk was based is totally revised. The subject arose from our feeling that work of Turaev and Virelizier [TV] on categorical structures graded by a group should exemplify the general theory of monoidal centres. The present talk will concentrate more on the general theory than the [TV] case. Our 2020 arXiv preprint made various claims about higher Davydov full centres with scant detail. Our revised version gives the much needed detail and that is what I hope to share in my talk.