Relative Regular Objects in Categories
范畴论
2007-05-23 v1 环与代数
摘要
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely generated Grothendieck categories. Applications are given for categories of comodules over a coalgebra and for categories of graded modules, and a link to the theory of generalized inverses of matrices is presented. Some of the techniques we use are new, since dealing with arbitrary categories allows us to pass to the dual category.
引用
@article{arxiv.math/0605606,
title = {Relative Regular Objects in Categories},
author = {S. S. Dăscălescu and C. Năstăsescu and A. Tudorache and L. Dăuş},
journal= {arXiv preprint arXiv:math/0605606},
year = {2007}
}