2006/05/23 by S. Dǎscǎlescu, S. S. Dăscălescu, C. Năstăsescu +8
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.CT #math.RA
paper · pdf · doi:10.48550/arxiv.math/0605606
arxiv created 2006/05/23 · openalex publication_date 2006/05/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.