  Gambino and Garner proved that the syntactic category of a dependent type
theory with identity types can be endowed with a weak factorization system
structure, called identity type weak factorization system. In this paper we
consider an enrichment of Joyal's notion of tribe, which we call a tribe with
weakly stable path objects, and prove a purely category-theoretic version of
the identity type weak factorization system, thus generalizing Gambino and
Garner's result. We conclude showing that this structure subsumes also the weak
factorization systems coming from the topological and simplicial models of
identity types obtained by van den Berg and Garner.
