Hardcover ISBN:  9783037192092 
Product Code:  EMSMONO/10 
List Price:  $65.00 
AMS Member Price:  $52.00 
Hardcover ISBN:  9783037192092 
Product Code:  EMSMONO/10 
List Price:  $65.00 
AMS Member Price:  $52.00 

Book DetailsEMS Monographs in MathematicsVolume: 10; 2020; 235 ppMSC: Primary 20; 18; 55; 19
This book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists.
The book contains an extended catalogue of examples of such Mackey 2functors that are already in use in many mathematical fields from algebra to topology, from geometry to KKtheory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples, and the separable monadicity theorem explains how the value of a Mackey 2functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology.
The second part of the book provides a motivic approach to Mackey 2functors, 2categorifying the wellknown span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshida's crossed Burnside ring are the universal source of block decompositions.
The book is selfcontained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interested in category theory, representation theory, and topology.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and advanced researchers interested in category theory, representation theory, and topology.

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This book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists.
The book contains an extended catalogue of examples of such Mackey 2functors that are already in use in many mathematical fields from algebra to topology, from geometry to KKtheory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples, and the separable monadicity theorem explains how the value of a Mackey 2functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology.
The second part of the book provides a motivic approach to Mackey 2functors, 2categorifying the wellknown span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshida's crossed Burnside ring are the universal source of block decompositions.
The book is selfcontained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interested in category theory, representation theory, and topology.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and advanced researchers interested in category theory, representation theory, and topology.