可定义子范畴的张量扩张与直接扩张
表示论
2026-03-31 v2 逻辑
摘要
可定义子范畴可沿环同态直接扩张（在新模范畴中使用其定义条件），或通过与新环作张量积来扩张。我们研究这些过程保持与反射了哪些性质。在此过程中，我们引入相对于双模为 Mittag-Leffler 的概念——这是对 Mittag-Leffler 条件的精细化。我们特别关注的是环同态为初等嵌入的情形。
引用
@article{arxiv.2305.08678,
title = {Tensor and direct extension of definable subcategories},
author = {Mike Prest},
journal= {arXiv preprint arXiv:2305.08678},
year = {2026}
}
备注
Definition 4.16 (4.15 in v1): the terminology has been changed ("atomic" replaced by "Mittag-Leffler") to fit better with existing terminology. Remark 4.22 (4.21 in v1): the example has been replaced with a correct example. Theorem 4.29 (4.15 in v1): the hypothesis has been strengthened from pure-projective to finitely presented. Plus some minor improvements