Monoidal Functors, Species and Hopf Algebras (Crm Monograph Series, 29) - Hardcover

Marcelo Aguiar; Swapneel Mahajan

Hardcover

ISBN 10: 0821847767 ISBN 13: 9780821847763

Publisher: American Mathematical Society, 2010

Synopsis

This research monograph integrates ideas from category theory, algebra and combinatorics. It is organized in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Bénabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal's species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the tex

About this edition

• Publisher: American Mathematical Society
• Publication date: 2010
• ISBN 10: 0821847767
• ISBN 13: 9780821847763
• Binding: Hardcover
• Number of pages: 784