Displaying similar documents to “On the category of n-groups”

Spaces associated to quadratic endofunctors of the category of groups.

Hans-Joachim Baues, Teimuraz Pirashvili (2005)

Extracta Mathematicae

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Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.

A short proof of Eilenberg and Moore’s theorem

Maria Nogin (2007)

Open Mathematics

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In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.