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Infinity Operads And Monoidal Categories With Group Equivariance (Hardcover)
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Infinity Operads And Monoidal Categories With Group Equivariance (Hardcover)
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This monograph provides a coherent development of operads, infinity
operads, and monoidal categories, equipped with equivariant
structures encoded by an action operad. A group operad is a planar
operad with an action operad equivariant structure. In the first
three parts of this monograph, we establish a foundation for group
operads and for their higher coherent analogues called infinity
group operads. Examples include planar, symmetric, braided, ribbon,
and cactus operads, and their infinity analogues. For example, with
the tools developed here, we observe that the coherent ribbon nerve
of the universal cover of the framed little 2-disc operad is an
infinity ribbon operad.In Part 4 we define general monoidal
categories equipped with an action operad equivariant structure and
provide a unifying treatment of coherence and strictification for
them. Examples of such monoidal categories include symmetric,
braided, ribbon, and coboundary monoidal categories, which
naturally arise in the representation theory of quantum groups and
of coboundary Hopf algebras and in the theory of crystals of finite
dimensional complex reductive Lie algebras.
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