Relatively divisible and relatively flat objects in exact categories: Applications
Septimiu Crivei, Derya Kesk\.in T\"ut\"unc\"u
TL;DR
This paper explores the properties of relatively divisible and flat objects within exact categories, providing new insights and applications to the structure of finitely accessible additive and module categories.
Contribution
It introduces new results on the behavior of these objects and applies them to specific exact structures related to simple modules and modules with zero Jacobson radical.
Findings
New characterizations of relatively divisible and flat objects
Applications to exact structures on module categories
Insights into the structure of finitely accessible additive categories
Abstract
We continue our study of relatively divisible and relatively flat objects in exact categories in the sense of Quillen with several applications to exact structures on finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical.
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