Tensor and direct extension of definable subcategories
Abstract
Definable subcategories may be extended along a ring homomorphism directly, by using their defining conditions in the new module category, or by tensoring up with the new ring. We investigate what is preserved and reflected by these processes. On the way, we introduce the notion of being Mittag-Leffler with respect to a bimodule - a refinement of the Mittag-Leffler condition. Particular attention is given to the case where the ring homomorphism is an elementary embedding.
Keywords
Cite
@article{arxiv.2305.08678,
title = {Tensor and direct extension of definable subcategories},
author = {Mike Prest},
journal= {arXiv preprint arXiv:2305.08678},
year = {2026}
}
Comments
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