Hi David, You'll find a lot of information on this sort of duoidal category and variations thereon in our paper "Intercategories: a framework for three-dimensional category theory" available as #53 at http://www.mscs.dal.ca/~pare/publications.html though there is no special name given for it there (as you were asking). Bob (&Marco) On 2016-10-06, at 4:48 PM, David Yetter wrote:
Is there already a name in the literature for the special instance of duoidal category in which one of the monoidal structures is cartesian? In particular the instance in which if # denotes the non-cartesian monoidal structure and x the cartesian, the lax middle-four interchange transformation has components
(A x B) # (C x D) ------> (A # B) x (C # D) ?
It has come up in my current student's dissertation work. An existing name and citations to papers using this specific type of duoidal category would be much appreciated.
Best Thoughts,
David Yetter
Professor of Mathematics
Kansas State University
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