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Internal crossed modules
 Georgian Math
"... on the occasion of his seventieth birthday Abstract. We introduce the notion of (pre)crossed module in a semiabelian category, and establish equivalences between internal reflexive graphs and precrossed modules, and between internal categories and crossed modules. ..."
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Cited by 22 (0 self)
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on the occasion of his seventieth birthday Abstract. We introduce the notion of (pre)crossed module in a semiabelian category, and establish equivalences between internal reflexive graphs and precrossed modules, and between internal categories and crossed modules.
Higher Hopf formulae for homology via Galois Theory
, 2007
"... We use Janelidze’s Categorical Galois Theory to extend Brown and Ellis’s higher Hopf formulae for homology of groups to arbitrary semiabelian monadic categories. Given such a category A and a chosen Birkhoff subcategory B of A, thus we describe the BarrBeck derived functors of the reflector of A on ..."
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Cited by 19 (15 self)
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We use Janelidze’s Categorical Galois Theory to extend Brown and Ellis’s higher Hopf formulae for homology of groups to arbitrary semiabelian monadic categories. Given such a category A and a chosen Birkhoff subcategory B of A, thus we describe the BarrBeck derived functors of the reflector of A onto B in terms of centralization of higher extensions. In case A
Commutator theory in strongly protomodular categories.
 Theory Appl. Categories
, 2004
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Higher central extensions and Hopf formulae
, 2009
"... Higher extensions and higher central extensions, which are of importance to nonabelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf formulae is obtained. ..."
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Cited by 9 (6 self)
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Higher extensions and higher central extensions, which are of importance to nonabelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf formulae is obtained.
CLOSEDNESS PROPERTIES OF INTERNAL RELATIONS I: A UNIFIED APPROACH TO MAL'TSEV, UNITAL AND SUBTRACTIVE CATEGORIES
, 2006
"... We study closedness properties of internal relations in finitely completecategories, which leads to developing a unified approach to: Mal'tsev categories, in the sense of A. Carboni, J. Lambek and M. C. Pedicchio, that generalize Mal'tsev varietiesof universal algebras; unital categories ..."
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Cited by 7 (6 self)
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We study closedness properties of internal relations in finitely completecategories, which leads to developing a unified approach to: Mal'tsev categories, in the sense of A. Carboni, J. Lambek and M. C. Pedicchio, that generalize Mal'tsev varietiesof universal algebras; unital categories, in the sense of D. Bourn, that generalize pointed J'onssonTarski varieties; and subtractive categories, introduced by the author, thatgeneralize pointed subtractive varieties in the sense of A. Ursini.
Protoadditive functors, derived torsion theories and homology
 J. Pure Appl. Algebra
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On satellites in semiabelian categories: Homology . . .
, 2009
"... Working in a semiabelian context, we use Janelidze’s theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with ..."
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Cited by 5 (2 self)
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Working in a semiabelian context, we use Janelidze’s theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out some examples.