Abstract: In the first talk, we introduced Tits' projection map for real hyperplane arrangements, and gave a purely combinatorial description of this map in the special case of braid arrangements.

In this talk, we will see how this projection map appears naturally in the Hopf theory for Joyal's category of combinatorial species, motivating us to generalize the definition of species from braid arrangements to Coxeter arrangements and further to hyperplane arrangements. This talk is based on the work of Aguiar and Mahajan.