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\(G\)-Categories
Robert Gordon
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Memoirs of the American Mathematical Society
1993; 129 pp; softcover
Volume: 101
ISBN-10: 0-8218-2543-7
ISBN-13: 978-0-8218-2543-3
List Price: US$32
Individual Members: US$19.20
Institutional Members: US$25.60
Order Code: MEMO/101/482
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A \(G\)-category is a category on which a group \(G\) acts. This work studies the \(2\)-category \(G\)-Cat of \(G\)-categories, \(G\)-functors (functors which commute with the action of \(G\) ) and \(G\)-natural transformations (natural transformations which commute with the \(G\)-action). There is particular emphasis on the relationship between a \(G\)-category and its stable subcategory, the largest sub-\(G\)-category on which \(G\) operates trivially. Also contained here are some very general applications of the theory to various additive \(G\)-categories and to \(G\)-topoi.

Readership

Researchers in representation theory and algebraic topology.

Table of Contents

  • \(G\)-Categories: The stable subcategory, \(G\)-limits and stable limits
  • Systems of isomorphisms and stably closed \(G\)-categories
  • Partial \(G\)-sets: \(G\)-adjoints and \(G\)-equivalence
  • Par\((G\)-set) and \(G\)-representability
  • Transversals
  • Transverse limits and representations of transversaled functors
  • Reflections and stable reflections
  • \(G\)-Cotripleability
  • The standard factorization of insertion
  • Cotripleability of stable reflectors
  • The case of \(\scr D^G\)
  • Induced stable reflections and their signatures
  • The \(\scr D^G\)-targeted case
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