Dear all, The following preprint is available on the arxiv. We would be really thankful for any comments or suggestions :) Symmeric self-adjoint Hopf categories and a categorical Heisenberg double Adam Gal, Elena Gal We define what we call a symmetric self-adjoint Hopf structure on a semisimple abelian category, which is an analog of Zelevinsky's positive self-adjoint Hopf algebra structure for categories. As examples we exhibit this structure on the categories of polynomial functors and equivariant polynomial functors and obtain a categorical manifestation of Zelevinsky's decomposition theorem involving them. It follows from the work of Zelevinsky that every positive self-adjoint Hopf algebra A admits a Fock space action of the Heisenberg double (A,A). We show that the notion of symmetric self-adjoint Hopf category leads naturally to the definition of a categorical analog of such an action and that every symmetric self-adjoint Hopf category admits such an action http://arxiv.org/abs/1406.3973 Best regards, Adam Gal [For admin and other information see: http://www.mta.ca/~cat-dist/ ]