19 Aug
2015
19 Aug
'15
7:31 p.m.
You ask,
Suppose you have a category with finite products, say T, and a symmetric monoidal category, say C. Let [T,C] be the category where
objects are symmetric monoidal functors from T to C, morphisms are monoidal natural transformations.
...
Should [T,C] also have some sort of "comultiplication"? What extra benefits do we get from T being cartesian?
Not entirely analogous, but the fundamental group of an Abelian group C is just an Abelian group ... no comultiplication, in general, even though the circle (the counterpart of T) is both a comonoid (one of the reasons [T,C] gets a monoid structure) and a monoid. Makes me wonder about your question. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]