Clarification and Coinduction of Tambara Functors
Algebraic Topology
2025-08-14 v2 Commutative Algebra
K-Theory and Homology
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 -theory of Tambara functors, field-like Tambara functors, and Nullstellensatzian clarified Tambara functors.
Keywords
Cite
@article{arxiv.2505.08066,
title = {Clarification and Coinduction of Tambara Functors},
author = {Noah Wisdom},
journal= {arXiv preprint arXiv:2505.08066},
year = {2025}
}
Comments
32 pages, comments welcome! Changes from previous version: cut out some background and parts of section 5 on ideals and Nakaoka spectra to appear in a different article