The Frobenius condition, right properness, and uniform fibrations
Artikel i vetenskaplig tidskrift, 2017

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.

Författare

Nicola Gambino

Christian Sattler

Logik och Typer

Journal of Pure and Applied Algebra

0022-4049 (ISSN)

Vol. 221 12 3027-3068

Ämneskategorier

Algebra och logik

Datavetenskap (datalogi)

DOI

10.1016/j.jpaa.2017.02.013

Mer information

Skapat

2023-11-15