Title: A triangulated category without models Author(s): Fernando Muro Author's e-mail address: fmuro@ub.edu Author's mailing address: Universitat de Barcelona, Facultat de Matemàtiques, Departament d'Àlgebra i Geometria, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain AMS classification number: 18E30, 55P42, 16E40 arXive submission number: math.KT/0703311 Abstract: We exhibit a triangulated category which is neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category.