Abstract
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.
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