**Memoirs of the American Mathematical Society**

1993;
129 pp;
Softcover

MSC: Primary 18;

Print ISBN: 978-0-8218-2543-3

Product Code: MEMO/101/482

List Price: $34.00

Individual Member Price: $20.40

**Electronic ISBN: 978-1-4704-0059-0
Product Code: MEMO/101/482.E**

List Price: $34.00

Individual Member Price: $20.40

# $G$-Categories

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*Robert Gordon*

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.

#### Table of Contents

# Table of Contents

## $G$-Categories

- Table of Contents v6 free
- Introduction vii8 free
- 1. G–Categories: The Stable Subcategory, G–Limits and Stable Limits 118 free
- 2. Systems of Isomorphisms and Stably Closed G–Categories 724
- 3. Partial G–Sets: G–Adjoints and G–Equivalence 1633
- 4. Par(G–Set) and G–Representability 2340
- 5. Transversals 3047
- 6. Transverse Limits and Representations of Transversaled Functors 4057
- 7. Reflections and Stable Reflections 5269
- 8. G–Cotripleability 6380
- 9. The Standard Factorization of Insertion 7390
- 10. Cotripleability of Stable Reflectors 8097
- 11. The Case of D[sup(G)] 88105
- 12. Induced Stable Reflections and their Signatures 98115
- 13. The D[sup(G)]–Targeted Case 112129
- References 128145

#### Readership

Researchers in representation theory and algebraic topology.