The local Joyal model structure

Nicholas J. Meadows

The Joyal model structure on simplicial sets is extended to a model structure on the simplicial presheaves on a small site, in which the cofibrations are monomorphisms and the weak equivalences are local (or stalkwise) Joyal equivalences. The model structure is shown to be left proper.

Keywords: simplicial presheaves, quasi-categories, model structure duality, trace, derivator, absolute colimit

2010 MSC: 18G30, 18F20, 55U35

Theory and Applications of Categories, Vol. 31, 2016, No. 24, pp 690-711.

Published 2016-08-02.

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