Dear David On 7 Oct 2016, at 6:48 AM, David Yetter <dyetter@ksu.edu<mailto:dyetter@ksu.edu>> wrote: 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) ? You mean, of course, (A x B) # (C x D) ------> (A # C) x (B # 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. I can't do much better than ``monoidal category with finite products''. Any such becomes duoidal in this way. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]