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arXiv · 2505.08066

Clarification and Coinduction of Tambara Functors

Noah Wisdom
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Abstract

Tambara functors are equivariant analogues of rings arising in representation theory and equivariant homotopy theory. We introduce the notion of a clarified Tambara functor and show that under mild conditions every Tambara functor admits a decomposition as a product of coinductions of clarified Tambara functors; projection onto the non-coinduced part defines a reflective localization we call clarification. Through this perspective we study Morita invariance and $K$-theory of Tambara functors, field-like Tambara functors, and Nullstellensatzian clarified Tambara functors.

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Noah Wisdom. 2025-05-12. Clarification and Coinduction of Tambara Functors. https://arxiv.org/abs/2505.08066

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