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25
Higher Hopf formulae for homology via Galois Theory, preprint math.AT/0701815
, 2007
"... 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 ..."
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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. Categ
"... on the occasion of his sixtieth birthday. ..."
Baer Invariants In SemiAbelian Categories I: General Theory
 GENERAL THEORY, THEORY AND APPLICATIONS OF CATEGORIES
, 2004
"... Extending the work of Fröhlich, Lue and FurtadoCoelho, we consider the theory of Baer invariants in the context of semiabelian categories. Several exact sequences, relative to a subfunctor of the identity functor, are obtained. We consider a notion of commutator which, in the case of abelianizatio ..."
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Cited by 3 (2 self)
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Extending the work of Fröhlich, Lue and FurtadoCoelho, we consider the theory of Baer invariants in the context of semiabelian categories. Several exact sequences, relative to a subfunctor of the identity functor, are obtained. We consider a notion of commutator which, in the case of abelianization, corresponds to Smith's. The resulting notion of centrality fits into Janelidze and Kelly's theory of central extensions. Finally we propose a notion of nilpotency, relative to a Birkhoff subcategory of a semiabelian category.
Higher central extensions and Hopf formulae
, 902
"... 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. 0 ..."
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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. 0
Relative commutator theory in varieties of Ωgroups
 J. Pure Appl. Algebra
"... We introduce a new notion of commutator which depends on a choice of subvariety in any variety of Ωgroups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules. Keywords: Commutator, Ωgroup, central extension, Pe ..."
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We introduce a new notion of commutator which depends on a choice of subvariety in any variety of Ωgroups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules. Keywords: Commutator, Ωgroup, central extension, Peiffer commutator 0
BAER INVARIANTS IN SEMIABELIAN CATEGORIES II: HOMOLOGY
 THEORY AND APPLICATIONS OF CATEGORIES
, 2004
"... This article treats the problem of deriving the reflector of a semiabelian ..."
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This article treats the problem of deriving the reflector of a semiabelian
THE THIRD COHOMOLOGY GROUP CLASSIFIES DOUBLE CENTRAL EXTENSIONS
, 2010
"... We characterise the double central extensions in a semiabelian category in terms of commutator conditions. We prove that the third cohomology group H3 (Z, A) of an object Z with coefficients in an abelian object A classifies the double central extensions of Z by A. ..."
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We characterise the double central extensions in a semiabelian category in terms of commutator conditions. We prove that the third cohomology group H3 (Z, A) of an object Z with coefficients in an abelian object A classifies the double central extensions of Z by A.
INITIAL NORMAL COVERS IN BIHEYTING TOPOSES
"... To Jiˇrí Rosick´y, on his sixtieth birthday Abstract. The dual of the category of pointed objects of a topos is semiabelian, thus is provided with a notion of semidirect product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. F ..."
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To Jiˇrí Rosick´y, on his sixtieth birthday Abstract. The dual of the category of pointed objects of a topos is semiabelian, thus is provided with a notion of semidirect product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes, actions are representable provided the topos admits an essential Boolean covering. This contains the case of Boolean toposes and toposes of presheaves. In the localic case, the representability of actions forces the topos to be biHeyting: the lattices of subobjects are both Heyting algebras and the dual of Heyting algebras. 1. Introducing the problem Given a semiabelian category V (see [3] or [12]), consider for every object G ∈ V
WEAKLY MAL'CEV CATEGORIES
"... 1. Introduction A weakly Mal'cev category (WMC) is defined by the following two axioms: 1. Existence of pullbacks of split epis along split epis. 2. Every induced canonical pair of morphisms into a pullback (see Definition 2.3), is ..."
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1. Introduction A weakly Mal'cev category (WMC) is defined by the following two axioms: 1. Existence of pullbacks of split epis along split epis. 2. Every induced canonical pair of morphisms into a pullback (see Definition 2.3), is