Day convolution

Summary

Day convolution is a tensor product on the category of set-valued functors on a small monoidal category. It is built from the tensor product of the source category. It makes the functor category into a closed monoidal category. The Yoneda embedding becomes a strong monoidal functor. So Day convolution is the universal way to extend a monoidal structure from a category to its category of set-valued functors. It generalizes the convolution of functions on a group and the Cauchy product of power series.