  We extend the arithmetic product of species of structures and symmetric
sequences studied by Maia and Mendez and by Dwyer and Hess to coloured
symmetric sequences and show that it determines a normal oplax monoidal
structure on the bicategory of coloured symmetric sequences. In order to do
this, we establish general results on extending monoidal structures to Kleisli
bicategories. Our approach uses monoidal double categories, which help us to
attack the difficult problem of verifying the coherence conditions for a
monoidal bicategory in an efficient way.
