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PreprintarXiv licencearXiv

Tao-Travkin equivalence revisited

  • Penghui Li
  • David Nadler
  • Yakov Varshavsky
  • Zhiwei Yun
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Abstract

We give a simpler proof of the theorem of J.~Tao and R.~Travkin saying that (the neutral block of) the affine Hecke category is the monoidal colimit of finite Hecke categories. The argument is axiomatized to apply to various sheaf-theoretic and group-theoretic contexts. We also prove an extension of the Tao-Travkin equivalence for the whole affine Hecke category as a Morita equivalence.

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Cite

BibTeXRIS
BibTeX
@misc{li2026taotravkin,
  title = {{Tao-Travkin equivalence revisited}},
  author = {Penghui Li and David Nadler and Yakov Varshavsky and Zhiwei Yun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05465},
  eprint = {2610.05465},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05465},
}
RIS
TY  - UNPB
TI  - Tao-Travkin equivalence revisited
AU  - Penghui Li
AU  - David Nadler
AU  - Yakov Varshavsky
AU  - Zhiwei Yun
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05465
UR  - https://arxiv.org/abs/2610.05465
AB  - We give a simpler proof of the theorem of J.~Tao and R.~Travkin saying that (the neutral block of) the affine Hecke category is the monoidal colimit of finite Hecke categories. The argument is axiomatized to apply to various sheaf-theoretic and group-theoretic contexts. We also prove an extension of the Tao-Travkin equivalence for the whole affine Hecke category as a Morita equivalence.
ER  -