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arXiv · 1304.3033

Some remarks on multicategories and additive categories

Claudio Pisani
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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.

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Claudio Pisani. 2013-04-10. Some remarks on multicategories and additive categories. https://arxiv.org/abs/1304.3033

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