Mackey 2-Functors and Mackey 2-Motives
Seiten
2020
EMS Press (Verlag)
978-3-03719-209-2 (ISBN)
EMS Press (Verlag)
978-3-03719-209-2 (ISBN)
This book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2-functors 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 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. 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 2-functor 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 2-functors, 2-categorifying the well-known 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 self-contained, 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.
The book contains an extended catalogue of examples of such Mackey 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. 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 2-functor 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 2-functors, 2-categorifying the well-known 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 self-contained, 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.
| Erscheinungsdatum | 31.08.2020 |
|---|---|
| Reihe/Serie | EMS Monographs in Mathematics |
| Verlagsort | Zurich |
| Sprache | englisch |
| Maße | 165 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | 2-functors • Ambidexterity • Burnside algebras • derivators • equivariant • Groupoids • Mackey formula • motivic decompositions • separable monadicity • spans • string diagrams |
| ISBN-10 | 3-03719-209-7 / 3037192097 |
| ISBN-13 | 978-3-03719-209-2 / 9783037192092 |
| Zustand | Neuware |
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