Coherent functors in stable homotopy theory

Henning Krause

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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.