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Combinatorial n-fold monoidal categories and n-fold operads

S. Forcey·J. Siehler·E. Seth Sowers
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Abstract

Operads were originally defined as V-operads, that is, enriched in a symmetric or braided monoidal category V. The symmetry or braiding in V is required in order to describe the associativity axiom the operads must obey, as well as the associativity that must be a property of the action of an operad on any of its algebras. After a review of the role of operads in loop space theory and higher categories we go over definitions of iterated monoidal categories and introduce a large family of simple examples. Then we generalize the definition of operad by defining n-fold operads and their algebras in an iterated monoidal category. We discuss examples of these that live in the previously described categories. Finally we describe the iterated monoidal category of m-fold V-operads.

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S. Forcey, J. Siehler, E. Seth Sowers. 2006-09-12. Combinatorial n-fold monoidal categories and n-fold operads. https://arxiv.org/abs/math/0411561

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