A structure theorem for 2-hypergroupoids with topological applications
ISSN: 0010-0757
Year of publication: 1985
Volume: 36
Fascicle: 1
Pages: 3-11
Type: Article
More publications in: Collectanea mathematica
Abstract
BRANDT [1] gave a structure theorem for connecte groupoids $G$, which in a simplicial version stablishes that $K(\Pi_1\quad (G,^\ast), \thinspace 1)$ is a strong deformation retract of $G$. The main object of this paper is to generalice Brandt's theorem to dimension tow: "If $G$ is a Kan 1-connected 2-hypergroupoid, $K(\Pi_2(G,^\ast), 2)$ is a strong deformation retract of $G$". Then, for a 1-connected topological space $X$ and $^\ast\epsilon X$ the homotopy 2-hypergroupoid of $X$ is equivalent to the second homotopy group $\Pi_2(X,^\ast)$ and the Hurewicz theorem is obtained as an elemental application.