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.
