me sense.
While it is often noted that the grading and action correspond exactly to the data of a functor,
the fact that virtually all of the structure needed to define operads can be expressed categorically is often passed by,
which I think is quite the shame!
In this post I want to explicitly calculate the Day convolution for symmetric operads in the category of
vector spaces—though the argument holds for all nice enough target categories—in order
to show that it is nothing but the usual tensor produc