東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Mackey 2-Functors and Mackey 2-Motives

Balmer, Paul,

Linked to FindBook

Google Book

Amazon

博客來

Mackey 2-Functors and Mackey 2-Motives

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mackey 2-Functors and Mackey 2-Motives/ Paul Balmer, Ivo Dell'Ambrogio
Author:	Balmer, Paul,
other author:	Dell'Ambrogio, Ivo,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2020,
Description:	1 online resource (235 pages)
Subject:	Mathematics and science -
Online resource:	https://doi.org/10.4171/209
Online resource:	https://www.ems-ph.org/img/books/balmer_mini.jpg
ISBN:	9783037197097

Mackey 2-Functors and Mackey 2-Motives
Balmer, Paul,

Mackey 2-Functors and Mackey 2-Motives[electronic resource] /Paul Balmer, Ivo Dell'Ambrogio - Zuerich, Switzerland :European Mathematical Society Publishing House,2020 - 1 online resource (235 pages) - EMS Monographs in Mathematics (EMM) ;2523-5192.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037197097

Standard No.: 10.4171/209doiSubjects--Topical Terms:

3481059
Mathematics and science

Mackey 2-Functors and Mackey 2-Motives
LDR:02527nmm a22003015a 4500 001 2233334
003 CH-001817-3
005 20200706233004.0
006 a fot ||| 0|
007 cr nn mmmmamaa
008 210928e20200804sz fot ||| 0|eng d
020 $a 9783037197097
024 7 0 $a 10.4171/209 $2 doi
035 $a 256-200706
040 $a ch0018173
072 7 $a P $2 bicssc
084 $a 20-xx $a 18-xx $a 19-xx $a 55-xx $2 msc
100 1 $a Balmer, Paul, $e author. $3 3481206
245 1 0 $a Mackey 2-Functors and Mackey 2-Motives $h [electronic resource] / $c Paul Balmer, Ivo Dell'Ambrogio
260 3 $a Zuerich, Switzerland : $b European Mathematical Society Publishing House, $c 2020
300 $a 1 online resource (235 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 0 $a EMS Monographs in Mathematics (EMM) ; $x 2523-5192
506 1 $a Restricted to subscribers: $u https://www.ems-ph.org/ebooks.php
520 $a 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.
650 0 7 $a Mathematics and science $2 bicssc $3 3481059
650 0 7 $a Group theory and generalizations $2 msc $3 3480853
650 0 7 $a Category theory; homological algebra $2 msc $3 3480981
650 0 7 $a $K$-theory $2 msc $3 3480892
650 0 7 $a Algebraic topology $v Congresses. $3 1575359
700 1 $a Dell'Ambrogio, Ivo, $e author. $3 3481207
856 4 0 $u https://doi.org/10.4171/209
856 4 2 $3 cover image $u https://www.ems-ph.org/img/books/balmer_mini.jpg