  This article presents three characterizations of the weak factorization
systems on finitely complete categories that interpret intensional dependent
type theory with Sigma-, Pi-, and Id-types. The first characterization is that
the weak factorization system (L,R) has the properties that L is stable under
pullback along R and that all maps to a terminal object are in R. We call such
weak factorization systems type-theoretic. The second is that the weak
factorization system has an Id-presentation: roughly, it is generated by
Id-types in the empty context. The third is that the weak factorization system
(L, R) is generated by a Moore relation system, a generalization of the notion
of Moore paths.
