2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127623We generalize and greatly simplify the approach of Lydakis and Dundas-Röndigs-Østvær to construct an L-stable model structure for small functors from a closed symmetric monoidal model category V to a V-model category M, where L is a small cofibrant object of V. For the special case V=M=S_* pointed simplicial sets and L=S^1 this is the classical case of linear functors and has been described as the first stage of the Goodwillie tower of a homotopy functor. We show, that our various model structures are compatible with a closed symmetric monoidal product on small functors. We compare them with other L-stabilizations described by Hovey, Jardine and others. This gives a particularly easy construction of the classical and the motivic stable homotopy category with the correct smash product. We establish the monoid axiom under certain conditions.39 pagesAlgebraic TopologyCategory Theory55P42, 55U35, 18D20, 55P91text