English

Relatively divisible and relatively flat objects in exact categories

Category Theory 2018-10-30 v1 Rings and Algebras

Abstract

We introduce and study relatively divisible and relatively flat objects in exact categories in the sense of Quillen. For every relative cotorsion pair (A,B)(\mathcal{A},\mathcal{B}) in an exact category C\mathcal{C}, A\mathcal{A} coincides with the class of relatively flat objects of C\mathcal{C} for some relative projectively generated exact structure, while B\mathcal{B} coincides with the class of relatively divisible objects of C\mathcal{C} for some relative injectively generated exact structure. We exhibit Galois connections between relative cotorsion pairs, relative projectively generated exact structures and relative injectively generated exact structures in additive categories. We establish closure properties and characterizations in terms of approximation theory.

Keywords

Cite

@article{arxiv.1810.11637,
  title  = {Relatively divisible and relatively flat objects in exact categories},
  author = {Septimiu Crivei and Derya Keskin Tütüncü},
  journal= {arXiv preprint arXiv:1810.11637},
  year   = {2018}
}

Comments

16 pages

R2 v1 2026-06-23T04:54:30.275Z