Picard groups, Grothendieck rings, and Burnside rings of categories. (English) Zbl 0994.18004
P. Freyd [Proc. Conf. Categorical Algebra, Springer-Verlag, New York, 121-172 (1966; Zbl 0195.52901)] said, “Perhaps the purpose of categorical algebra is to show that which is trivial is trivially trivial”. However, the author of this article prefers an update of that quote: “Perhaps the purpose of categorical algebra is to show that which is formal is formally formal”. In this article, the author gives a nice discussion of the Picard group, the Grothendieck ring, and the Burnside ring of a symmetric monoidal category, and exhibit many examples from algebra, homological algebra, topology, and algebraic geometry. The list of references is useful.
Reviewer: Li Fu-an (Beijing)
MSC:
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
| 19A22 | Frobenius induction, Burnside and representation rings |
| 18F25 | Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) |
Citations:
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