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arxiv: 1205.2516 · v1 · submitted 2012-05-11 · 🧮 math.AT

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Tambara functors

Neil Strickland

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keywords functorsringsexampleshomotopymapstambaratheoryabstract
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We survey and extend the theory of Tambara functors. These are algebraic structures similar to Mackey functors, but with multiplicative norm maps as well as additive transfer maps, and a rule governing their interaction that is most easily formulated in an abstract categorical framework. Examples include Burnside rings, representation rings, and homotopy groups of equivariant E-infinity ring spectra in stable homotopy theory. Some other examples are related to Witt rings in the sense of Dress and Siebeneicher.

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Cited by 2 Pith papers

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  1. Spectra of bi-incomplete Tambara functors

    math.AT 2026-05 unverdicted novelty 7.0

    The spectrum of prime ideals is defined for arbitrary bi-incomplete Tambara functors, generalizing Lewis's and Nakaoka's notions for Green and Tambara functors.

  2. A point-free approach to the Nakaoka spectrum of a Tambara functor

    math.AT 2026-04 unverdicted novelty 6.0

    Constructs the frame RadId_G(T) of radical Tambara ideals whose points are the Nakaoka primes and deduces that the Nakaoka spectrum is a spectral space.