The Frobenius condition, right properness, and uniform fibrations

Nicola Gambino, Christian Sattler

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)3027-3068
Number of pages42
JournalJ. Pure Appl. Algebra
Issue number12
Publication statusPublished - Dec 2017


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