Memoirs of the American Mathematical Society 1993; 129 pp; softcover Volume: 101 ISBN10: 0821825437 ISBN13: 9780821825433 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/101/482
 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
