PreprintCC BY 4.0arXiv
Koszul duality for boundary categories
Abstract
We study how Koszul duality relates two kinds of boundary constructions associated with a smooth category and a proper category. For a smooth category with a proper Koszul-dualizing subcategory, we construct a fully faithful functor from its categorical neighborhood of infinity to the singularity category associated to the proper category. We prove that this functor is an equivalence precisely when the smooth category is reflexive, meaning that it can be reconstructed from its finite-dimensional module theory. Under a Gorenstein condition, satisfied in the Calabi--Yau setting, the functor is induced by restriction of modules. We give algebraic criteria that ensure equivalence and obtain an identification of Hochschild cohomology.
Related
- Koszul duality for finite-dimensional absolutely Koszul algebras
- Koszul Duality in an Equivariant Context
- Diagonalizable modular derivations on bigraded Poisson spaces and Koszul duality
- Koszul Duality for Symmetric Algebras and Derived Loop Spaces
- An explicit Dennis trace and its compatibility with Koszul duality
BibTeX
@misc{gao2026koszul,
title = {{Koszul duality for boundary categories}},
author = {Yuan Gao and Zhen Gao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02080},
eprint = {2611.02080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02080},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Koszul duality for boundary categories
AU - Yuan Gao
AU - Zhen Gao
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02080
UR - https://arxiv.org/abs/2611.02080
AB - We study how Koszul duality relates two kinds of boundary constructions associated with a smooth category and a proper category. For a smooth category with a proper Koszul-dualizing subcategory, we construct a fully faithful functor from its categorical neighborhood of infinity to the singularity category associated to the proper category. We prove that this functor is an equivalence precisely when the smooth category is reflexive, meaning that it can be reconstructed from its finite-dimensional module theory. Under a Gorenstein condition, satisfied in the Calabi--Yau setting, the functor is induced by restriction of modules. We give algebraic criteria that ensure equivalence and obtain an identification of Hochschild cohomology.
ER -