Infinity Operads And Monoidal Categories With Group Equivariance
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A01=Donald Yau
Action Operads
Author_Donald Yau
Braided Monoidal Categories
Braided Operads
Cactus Operads
Category=PBMW
Coboundary Monoidal Categories
Coherence
Coherent Nerves
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Group Operads
Infinity Operads
Little Disc Operad
Monoidal Categories
Operads
Ribbon Operads
Strictification
Symmetric Monoidal Categories
Product details
- ISBN 9789811250927
- Publication Date: 23 Dec 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
