English

Exact subcategories, subfunctors of $\operatorname{Ext}$, and some applications

Category Theory 2023-10-31 v3 Commutative Algebra Representation Theory

Abstract

Let (A,E)(\mathcal{A},\mathcal{E}) be an exact category. We establish basic results that allow one to identify sub(bi)functors of ExtE(,)\operatorname{Ext}_{\mathcal{E}}(-,-) using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in details, and find a range of applications from detecting regularity to understanding Ulrich modules.

Keywords

Cite

@article{arxiv.2205.15297,
  title  = {Exact subcategories, subfunctors of $\operatorname{Ext}$, and some applications},
  author = {Hailong Dao and Souvik Dey and Monalisa Dutta},
  journal= {arXiv preprint arXiv:2205.15297},
  year   = {2023}
}

Comments

To appear in Nagoya Mathematical Journal. This arXiv version contains one additional result (than the Journal Version), namely Proposition 5.1.27