Species, convolution, and bimonoidal structure

Steve Lack – 14 February 2018

This talk is based on aspects of the Aguiar-Mahajan book "Monoidal functors, species, and Hopf algebras", and of the Aguiar-Ardilar preprint "Hopf monoids and generalized permutahedra". Depending on the level of interest, I may give further talks on the subject.

I will define species in Set, in Vect, and in a general symmetric monoidal category V, as well as giving some examples of these. I will define bimonoidal species in each case. I will describe the convolution product of species, and the extent to which it can be used to talk about bimonoidal structure. Finally I will say a bit about antipodes and the overall structure of the references cited above.