| Description |
1 online resource (235 pages). |
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text file PDF |
| Series |
EMS Monographs in Mathematics (EMM) ;
2523-5192
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| Summary |
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 interestedin category theory, representation theory and topology. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematics and science. |
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Group theory and generalizations. |
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Category theory; homological algebra. |
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$K$-theory. |
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Algebraic topology. |
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Functor theory.
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Functor theory. |
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Homology theory.
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Homology theory. |
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Finite groups.
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Finite groups. |
| Genre/Form |
Electronic books.
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Technical reports.
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Technical reports.
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| Added Author |
Dell'Ambrogio, Ivo, author.
|
| ISBN |
9783037197097 |
|
3037197099 |
| Standard No. |
10.4171/209 |
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