Abstract. The category of bisimplicial presheaves carries a model structure for which the weak equivalences are defined by the diagonal functor and the cofibrations are monomorphisms. This model structure has the most cofibrations of a large family of model structures with weak equivalences defined by the diagonal. The diagonal structure for bisimplicial presheaves specializes to a diagonal model structure for bisimplicial sets, for which the fibrations are the Kan fibrations
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