| eBook ISBN: | 978-1-4704-0059-0 |
| Product Code: | MEMO/101/482.E |
| List Price: | $34.00 |
| MAA Member Price: | $30.60 |
| AMS Member Price: | $20.40 |
| eBook ISBN: | 978-1-4704-0059-0 |
| Product Code: | MEMO/101/482.E |
| List Price: | $34.00 |
| MAA Member Price: | $30.60 |
| AMS Member Price: | $20.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 101; 1993; 129 ppMSC: Primary 18
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.
ReadershipResearchers in representation theory and algebraic topology.
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Table of Contents
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Chapters
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1. $G$-categories: The stable subcategory, $G$-limits and stable limits
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2. Systems of isomorphisms and stably closed $G$-categories
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3. Partial $G$-sets: $G$-adjoints and $G$-equivalence
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4. Par($G$-set) and $G$-representability
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5. Transversals
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6. Transverse limits and representations of transversaled functors
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7. Reflections and stable reflections
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8. $G$-cotripleability
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9. The standard factorization of insertion
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10. Cotripleability of stable reflectors
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11. The case of $\mathcal {D}^G$
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12. Induced stable reflections and their signatures
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13. The $\mathcal {D}^G$-targeted case
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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.
Researchers in representation theory and algebraic topology.
-
Chapters
-
1. $G$-categories: The stable subcategory, $G$-limits and stable limits
-
2. Systems of isomorphisms and stably closed $G$-categories
-
3. Partial $G$-sets: $G$-adjoints and $G$-equivalence
-
4. Par($G$-set) and $G$-representability
-
5. Transversals
-
6. Transverse limits and representations of transversaled functors
-
7. Reflections and stable reflections
-
8. $G$-cotripleability
-
9. The standard factorization of insertion
-
10. Cotripleability of stable reflectors
-
11. The case of $\mathcal {D}^G$
-
12. Induced stable reflections and their signatures
-
13. The $\mathcal {D}^G$-targeted case
