PreprintCC BY 4.0arXiv
Homological and homotopical epimorphisms in monoidal ∞-categories
Abstract
We compare homological and homotopical epimorphisms of associative algebras in monoidal ∞-categories. Assume that geometric realizations and pushouts of associative algebras exist and that tensoring preserves geometric realizations. Then every homological epimorphism is homotopical. If, in addition, the ambient category is additive and tensoring preserves finite coproducts, the converse holds. This extends the result of Chuang and Lazarev for dg-algebras. In the symmetric monoidal setting, we discuss consequences for centers and commutative refinements, as well as applications to derived analytic geometry.
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BibTeX
@misc{bambozzi2026homological,
title = {{Homological and homotopical epimorphisms in monoidal $\infty$-categories}},
author = {Federico Bambozzi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34592},
eprint = {2610.34592},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34592},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Homological and homotopical epimorphisms in monoidal ∞-categories
AU - Federico Bambozzi
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34592
UR - https://arxiv.org/abs/2610.34592
AB - We compare homological and homotopical epimorphisms of associative algebras in monoidal ∞-categories. Assume that geometric realizations and pushouts of associative algebras exist and that tensoring preserves geometric realizations. Then every homological epimorphism is homotopical. If, in addition, the ambient category is additive and tensoring preserves finite coproducts, the converse holds. This extends the result of Chuang and Lazarev for dg-algebras. In the symmetric monoidal setting, we discuss consequences for centers and commutative refinements, as well as applications to derived analytic geometry.
ER -