  We consider the composition product of symmetric sequences in the case where
the underlying symmetric monoidal structure does not commute with coproducts.
Even though this composition product is not a monoidal structure on symmetric
sequences, it has enough structure, namely that of a `normal oplax' monoidal
product, to be able to define monoids (which are then operads on the underlying
category) and make a bar construction. The main benefit of this work is in the
dual setting, where it allows us to define a cobar construction for cooperads.
