Baer-Kaplansky classes in categories: transfer via functors

S Crivei, DK Tütüncü, R Tribak - Communications in Algebra, 2020 - Taylor & Francis
We study the transfer of Baer-Kaplansky classes via additive functors between preadditive
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …

Baer–Kaplansky classes in Grothendieck categories and applications

S Crivei, D Keskin Tütüncü - Mediterranean Journal of Mathematics, 2019 - Springer
Abstract We study Baer–Kaplansky classes in Grothendieck categories. We apply our results
to functor categories, and discuss the transfer of the Baer–Kaplansky property to finitely …

Pure-direct-objects in categories: transfer via functors

SE Toksoy - Communications in Algebra, 2023 - Taylor & Francis
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Transfer of CS-Rickart and dual CS-Rickart properties via functors between abelian categories

S Crivei, SM Radu - Quaestiones Mathematicae, 2022 - Taylor & Francis
We study the transfer of (dual) relative CS-Rickart properties via functors between abelian
categories. We consider fully faithful functors as well as adjoint pairs of functors. We give …

Strongly Rickart objects in abelian categories: Applications to strongly regular and strongly Baer objects

S Crivei, G Olteanu - Communications in Algebra, 2018 - Taylor & Francis
We show how the theory of (dual) strongly relative Rickart objects may be employed in order
to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian …

Rickart and dual Rickart objects in abelian categories: Transfer via functors

S Crivei, G Olteanu - Applied Categorical Structures, 2018 - Springer
We study the transfer of (dual) relative Rickart properties via functors between abelian
categories, and we deduce the transfer of (dual) relative Baer property. We also give …

[HTML][HTML] A generalization of the Gabriel–Popescu theorem

W Lowen - Journal of Pure and Applied Algebra, 2004 - Elsevier
In this paper we give necessary and sufficient conditions for an additive functor u: u→ C,
from a small pre-additive category u to a Grothendieck category C, to realize C as a …

On Some Noteworthy Pairs of Ideals in Mod-R

A Facchini, M Perone - Applied Categorical Structures, 2014 - Springer
An additive functor F:\mathcalA→\mathcalB between preadditive categories \mathcalA and
\mathcalB is said to be a local functor if, for every morphism f:A→A' in \mathcalA, F (f) …

Strongly Rickart objects in abelian categories

S Crivei, G Olteanu - Communications in Algebra, 2018 - Taylor & Francis
We introduce and study (dual) strongly relative Rickart objects in abelian categories. We
prove general properties, we analyze the behaviour with respect to (co) products, and we …

Profunctors in Mal'tsev categories and fractions of functors

S Mantovani, G Metere, EM Vitale - Journal of Pure and Applied Algebra, 2013 - Elsevier
We study internal profunctors and their normalization under various conditions on the base
category. In the Mal'tsev case we give an easy characterization of profunctors. Moreover …