Document Zbl 0887.18005 - zbMATH Open
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Schreier theory for central extensions of categorical groups. (English) Zbl 0887.18005
The aim of the paper is to show that the well known group theoretic interpretations of homotopy classes of maps between Eilenberg-MacLane spaces are particular cases of more general results.
By means of [L. Breen, Ann. Sci. Èc. Norm. Supér., IV. Sér. 25, No. 5, 465-514 (1992; Zbl 0795.18009) and R. Lavendhomme, Séminaire d’algébre catégorique, Louvain (1966)] the authors give a suitable definition of a central extension of a categorical group by a braided categorical group and show that these extensions are classified by an appropriate cohomology set. Then, using the companion paper [the authors, Commun. Algebra 24, No. 13, 3995-4058 (1996; see the review above)] the homotopy classes of maps from a space with the homotopy type of a categorical group to a space with the homotopy type of a braided group are interpreted in terms of these central extensions of associated categorical groups.