  A relative category is a category with a chosen class of weak equivalences.
Barwick and Kan produced a model structure on the category of all relative
categories, which is Quillen equivalent to the Joyal model structure on
simplicial sets and the Rezk model structure on simplicial spaces. We will
prove that the underlying relative category of a model category or even a
fibration category is fibrant in the Barwick--Kan model structure.
