  We study generalized automata (in the sense of Ad\'amek-Trnkov\'a) in Joyal's
category of (set-valued) combinatorial species, and as an important preliminary
step, we study coalgebras for its derivative endofunctor $\partial$ and for the
`Euler homogeneity operator' $L\circ\partial$ arising from the adjunction
$L\dashv\partial\dashv R$.
