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Coends and the tensor product of $\mathcal{C}$-modules

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arxiv 1608.02828 v3 pith:BCHO64WU submitted 2016-08-09 math.CT

Marco A. Pérez This is my paper · ORCID
classification math.CT
keywords extensionsproducttensorcoendsconceptfunctorsmathcalmodules
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abstract

We give an introduction to the concept of Kan extensions, and study its relation with the notions of coend and adjoint functors. We state and prove in detail a well known formula to compute Kan extensions by using coends: a certain colimit related to the concept of copower. Finally, we study the tensor product of functors, and its relation with Kan extensions, in order to represent the tensor product of $\mathcal{C}$-modules as a particular case.

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