  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.
