A note on the composition product of symmetric sequences

Details A note on the composition product of symmetric sequences A note on the composition product of symmetric sequences

2005-10-23

arxiv.org/abs/math/0510490v2

Mathematics

Category Theory

many changes, 15 pages, version to appear in Journal of Homotopy and Related Structures

Scientific paper

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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