A model structure whose fibrant objects are internal quasi-categories

Dominic Verity – 11 April 2007

Much of the "category theory" of weak complicial sets is best cast in terms of a certain kind of internal quasi-category theory. In this talk we show how to define such internal quasi-categories within any suitably well behaved model category M. Furthermore, as a first step to developing the category theory of such structures, we build a natural model structure on the category of simplicial objects in M whose fibrant objects are precisely the quasi-categories internal to M.