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PreprintCC BY 4.0arXiv

The coanalyticity of the reduced K-theory on modules over free tensor algebras of dualizable t-categories

  • Li He
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Abstract

In this paper, we formulate Land-Tamme's boxtimes-construction and ⊙-construction for continuous exact monads on dualizable stable ∞-categories, and establish the behaviour of localizing invariants on pushouts of left modules over continuous exact monads on dualizable stable ∞-categories. Combining the Land-Tamme theory of continuous exact monads with the theory of analytic functors in Goodwillie calculus, we show that the reduced K-theory on modules over free tensor algebras of dualizable t-categories is modified 1-coanalytic or modified 2-coanalytic, depending on the coconnectivity of the base algebras. In particular, this answers Efimov's question concerning coanalyticity in the affirmative.

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Cite

BibTeXRIS
BibTeX
@misc{he2026coanalyticity,
  title = {{The coanalyticity of the reduced K-theory on modules over free tensor algebras of dualizable t-categories}},
  author = {Li He},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41566},
  eprint = {2610.41566},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41566},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The coanalyticity of the reduced K-theory on modules over free tensor algebras of dualizable t-categories
AU  - Li He
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41566
UR  - https://arxiv.org/abs/2610.41566
AB  - In this paper, we formulate Land-Tamme's boxtimes-construction and ⊙-construction for continuous exact monads on dualizable stable ∞-categories, and establish the behaviour of localizing invariants on pushouts of left modules over continuous exact monads on dualizable stable ∞-categories. Combining the Land-Tamme theory of continuous exact monads with the theory of analytic functors in Goodwillie calculus, we show that the reduced K-theory on modules over free tensor algebras of dualizable t-categories is modified 1-coanalytic or modified 2-coanalytic, depending on the coconnectivity of the base algebras. In particular, this answers Efimov's question concerning coanalyticity in the affirmative.
ER  -