Coends and the tensor product of $\mathcal{C}$-modules
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 -modules as a particular case.
Cite
@article{arxiv.1608.02828,
title = {Coends and the tensor product of $\mathcal{C}$-modules},
author = {Marco A. Pérez},
journal= {arXiv preprint arXiv:1608.02828},
year = {2016}
}
Comments
37 pages, 42 figures. Some terminology mistakes in the first version were fixed. Typos corrected. The formula to compute Kan extensions using coends was slightly generalized from small categories to skeletally small categories. Versions 2 and 1 in Spanish. Versions 2 and 3 are the same but in different languages