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.

Keywords: bisimplicial presheaves, diagonal functor, model structure

2010 MSC: Primary 18G30; Secondary 18F20, 55U35

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 10, pp 250-268.

Published 2013-05-16.

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