You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Reuben Stern (they/them) (Nov 17 2023 at 15:16):A duoidal category is a category equipped with a lax-commuting pair of monoidal structures. This feels like the kind if thing that should be expressable as an algebra over a "2-operad." Furthermore, it feels like this 2-operad should be expressable as a "lax BV-tensor product" of the associative operad with itself.
Is there a legitimate story here? My super general hope would be for a theory of n-operad for all n where there are inclusions that admit both left and right adjoints, under which the 2-operad parametrizing duoidal structures gets taken to either the operad or the operad . Furthermore, this theory should somehow extend the Gray tensor product.
Todd Trimble (Nov 17 2023 at 16:28):Reuben, have you been in touch with Zbigniew Fiedorowicz about this question?
Reuben Stern (they/them) (Nov 17 2023 at 18:42):I haven't -- have they done work on this?
Todd Trimble (Nov 17 2023 at 21:10):The topic smells related to their iterated monoidal categories, and so I thought possibly they've thought about this sort of thing.