A structure theorem for 2-hypergroupoids with topological applications

Autores: María Pilar Carrasco Carrasco , Antonio Martínez Cegarra , J. Olmos
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 36, Fasc. 1, 1985, págs. 3-11
Idioma: inglés
Títulos paralelos:
- Un teorema de estructura para 2-hipergrupoides con aplicaciones topológicas
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Resumen
- 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.