Infinity Properads and Infinity Wheeled Properads
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Beschreibung
The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads, and enable one to encode bialgebraic, rather than just (co)algebraic, structures.
The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study of operads and properads. A preliminary list of potential applications and extensions comprises the final chapter.
Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields of topology, algebra, category theory, and related areas. It is written roughly at the second year graduate level, and assumes a basic knowledge of category theory.
The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather than just (co)algebraic, structures.
The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study of operads and properads. A preliminary list of potential applications and extensions comprises the final chapter.
Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields of topology, algebra, category theory, and related areas. It is written roughly at the second year graduate level, and assumes a basic knowledge of category theory.
Studies topics that are somewhat ignored in the existent literature on properads Contains important results, especially concerning the combinatorics of graphs and graphs substitution Analyses technical and conceptual difficulties in an easy-to-read manner
Autor*in
Philip Hackney
Themen in »Infinity Properads and Infinity Wheeled Properads«
Fundamental Properad Graphical Sets Infinity-Properads Infinity-Wheeled Properads Properadic Nerve Properadic Segal Map Properads Symmetric Monoidal Categories Wheeled Properads
Stimmen zu »Infinity Properads and Infinity Wheeled Properads«
“This monograph gives a very nice and complete presentation of the theory of ∞-properads and ∞-wheeled properads. … This book is very well written, motivated and almost self-contained. It should be of high interest for people working in homotopy theory and higher categories.” (David Chataur, Mathematical Reviews, December, 2016)
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