2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209634We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, ``functors between two homotopy theories form a homotopy theory'', or more precisely that the category of such models has a well-behaved internal hom-object.revisions for publication, to appear in AMS TransAlgebraic TopologyCategory Theory55U35 (Primary), 18G30 (Secondary)text