  We develop further the theory of weak factorization systems and algebraic
weak factorization systems. In particular, we give a method for constructing
(algebraic) weak factorization systems whose right maps can be thought of as
(uniform) fibrations and that satisfy the (functorial) Frobenius condition. As
applications, we obtain a new proof that the Quillen model structure for Kan
complexes is right proper, avoiding entirely the use of topological realization
and minimal fibrations, and we solve an open problem in the study of
Voevodsky's simplicial model of type theory, proving a constructive version of
the preservation of Kan fibrations by pushforward along Kan fibrations. Our
results also subsume and extend work by Coquand and others on cubical sets.
