Relative Regular Objects in Categories |
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| Authors: | S Dăscălescu C Năstăsescu A Tudorache L Dăuş |
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| Institution: | (1) University of Bucharest, Facultatea de Matematică, Str. Academiei 14, Bucharest 1, RO-010014, Romania;(2) Universitatea de Ştiinţe Economice, Bucharest, Romania;(3) Universitatea de Construcţii, Bucharest, Romania |
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| Abstract: | 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.
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| Keywords: | arbitrary category abelian categories Grothendieck categories |
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