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A homotopical enhancement of Neisendorfer's algebraic models

  • Bruno Stonek
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Abstract

We give an ∞-categorical enhancement of Neisendorfer's equivalences between the homotopy categories of rational simplicial sets, commutative dg algebras (cdgas), cocommutative dg coalgebras (cdgcs) and dg Lie algebras (dgls), where these objects have respective hypotheses of connectedness, nilpotency and finite type. We do so by proving that linear duality is a partial Quillen equivalence between weak finite type connected cdgcs and cdgas, and that Quillen's Chevalley--Eilenberg adjunction is a partial crossed derivable equivalence between cdgcs and dgls, a concept we introduce in this paper to axiomatize precisely the behavior of this adjunction.

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Cite

BibTeXRIS
BibTeX
@misc{stonek2026homotopical,
  title = {{A homotopical enhancement of Neisendorfer's algebraic models}},
  author = {Bruno Stonek},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01350},
  eprint = {2610.01350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01350},
}
RIS
TY  - UNPB
TI  - A homotopical enhancement of Neisendorfer's algebraic models
AU  - Bruno Stonek
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01350
UR  - https://arxiv.org/abs/2610.01350
AB  - We give an ∞-categorical enhancement of Neisendorfer's equivalences between the homotopy categories of rational simplicial sets, commutative dg algebras (cdgas), cocommutative dg coalgebras (cdgcs) and dg Lie algebras (dgls), where these objects have respective hypotheses of connectedness, nilpotency and finite type. We do so by proving that linear duality is a partial Quillen equivalence between weak finite type connected cdgcs and cdgas, and that Quillen's Chevalley--Eilenberg adjunction is a partial crossed derivable equivalence between cdgcs and dgls, a concept we introduce in this paper to axiomatize precisely the behavior of this adjunction.
ER  -