Astérisque
Volume: 387;
2017;
161 pp;
Softcover
MSC: Primary 18; 55; 81; 16;
Print ISBN: 978-2-85629-852-7
Product Code: AST/387
List Price: $60.00
AMS Member Price: $48.00
Feynman Categories
Share this pageRalph M. Kaufmann; Benjamin C. Ward
A publication of the Société Mathématique de France
In this book, the authors give a new foundational, categorical
formulation for operations and relations and objects parameterizing
them. This generalizes and unifies the theory of operads and all their
cousins including but not limited to PROPs, modular operads, twisted
(modular) operads, properads, hyperoperads, their colored versions, as
well as algebras over operads and an abundance of other related
structures, such as crossed simplicial groups, the augmented
simplicial category or FI-modules.
The usefulness of this approach is that it allows the authors to
handle all the classical as well as more esoteric structures under a
common framework and treat all the situations simultaneously. Many of
the known constructions simply become Kan extensions. In this common
framework, the authors also derive universal operations, such as those
underlying Deligne's conjecture, construct Hopf algebras, as well as
perform resolutions, (co)bar transforms and Feynman transforms which
are related to master equations. For these applications, the authors
construct the relevant model category structures. This produces many
new examples.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Readership
Graduate students and research mathematicians.