* New preprint on multicategories
@ 2013-04-11 5:33 claudio pisani
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From: claudio pisani @ 2013-04-11 5:33 UTC (permalink / raw)
To: categories
Dear categorists,
the following preprint, now available on arXiv, is related to a recent discussion on this list and may be of interest to some of you:
Some remarks on multicategories and additive categories
Abstract:
Categories are coreflectively embedded in multicategories via the "discrete cocone" construction, the right adjoint being given by the monoid construction.
Furthermore, the adjunction lifts to the "cartesian level": preadditive categories are coreflectively embedded (as theories for many-sorted modules) in cartesian multicategories (general algebraic theories).
In particular, one gets a direct link between two ways of considering modules over a rig, namely as additive functors valued in commutative monoids or as models of the theory generated by the rig itself.
Comments are of course welcome. I also hope that someone will help me to fill the gap in the proof of proposition 3.8.
Best regards,
Claudio
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