2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128915In this article we build a Quillen model category structure on the category of sequentially complete l.m.c.-C*-algebras such that the corresponding homotopy classes of maps Ho(A,B) for separable C*-algebras A and B coincide with the Kasparov groups KK(A,B). This answers an open question posed by Mark Hovey about the possibility of describing KK-theory for C*-algebras using the language of Quillen model categories.Appeared in Contemporary Math #399: An Alpine Anthology of Homotopy Theory, Dominique Arlettaz and Katherine Hess editorsK-Theory and HomologyAlgebraic Topology46L80; 55U35text