Infinity Operads And Monoidal Categories With Group Equivariance (Hardcover)

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.

General

Imprint:	World Scientific Publishing Co Pte Ltd
Country of origin:	Singapore
Release date:	December 2021
First published:	2022
Authors:	Donald Yau
Format:	Hardcover
Pages:	488
ISBN-13:	978-981-12-5092-7
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	981-12-5092-8
Barcode:	9789811250927

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