Universal co-Extensions of torsion abelian groups

2022/06/17 by Argudín-Monroy, Alejandro, Parra, Carlos E. · 1 citation
#18E10 #18G15 #20K10 #20K25 #20K35 #20K40 #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2206.08857

Abstract

In [16], a theory of universal extensions in abelian categories is developed; in particular, the notion of Ext-universal object is presented. In the present paper, we show that an Ab3 abelian category which is Ext-small satisfies the Ab4 condition if, and only if, each one of its objects is Ext-universal. We also give a characterization of the co-Ext-universal objects of the category of torsion abelian groups. In particular, we show that such groups are the ones admitting a decomposition Q⊕ R, in which Q is injective and R is a reduced group on which each p-component is bounded.

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• Locally finitely presented Grothendieck categories with a flat generator

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