  We introduce a notion of extraction-contraction coproduct on twisted
bialgebras, that is to say bialgebras in the category of linear species. If $P$
is a twisted bialgebra, a contraction-extraction coproduct sends $P[X]$ to
$P[X/\sim]\otimes P[X]$ for any finite set $X$ and any equivalence relation
$\sim$ on $X$, with a coassociativity constraint and compatibilities with the
product and coproduct of $P$. We prove that if $P$ is a twisted bialgebra with
an extraction-contraction coproduct, then $P\circ Com$ is a bialgebra in the
category of coalgebraic species, that is to say species in the category of
coalgebras.We then introduce a coloured version of the bosonic Fock functor.
This induces a bifunctor which associates to any bialgebra $(V,\cdot,\delta_V)$
and to any twisted bialgebra $P$ with an extraction-contraction coproduct a
comodule-bialgebra $F_V[P]$: this object inherits a product $m$ and two
coproducts $\Delta$ and $\delta$, such that $(F_V[P],m,\Delta)$ is a bialgebra
in the category of right $(F_V[P],m,\delta)$-comodules.As an example, this is
applied to the twisted bialgebra of graphs. The coloured Fock functors then
allow to extend the construction of the double bialgebra of graphs to double
bialgebras of graphs which vertices are decorated by elements of any bialgebra
$V$. Other examples (on mixed graphs, hypergraphs, noncrossing partitions...)
will be given in a series of forthcoming papers.
