Frobenius 条件、右恰当性与一致纤维化
范畴论
2017-09-29 v5 代数拓扑
逻辑
摘要
我们进一步发展了弱因式分解系统与代数弱因式分解系统的理论。特别地，我们给出了一种构造（代数）弱因式分解系统的方法，其右映射可视为（一致）纤维化并满足（函子的）Frobenius 条件。作为应用，我们获得了 Kan 复形的 Quillen 模型结构是右恰当的这一结论的新证明，完全避免使用拓扑实现与极小纤维化；并且我们解决了 Voevodsky 的类型论单纯模型研究中的一个开放问题，证明了沿 Kan 纤维化推前保持 Kan 纤维化的构造性版本。我们的结果还包含并扩展了 Coquand 等人关于立方集的工作。
引用
@article{arxiv.1510.00669,
title = {The Frobenius Condition, Right Properness, and Uniform Fibrations},
author = {Nicola Gambino and Christian Sattler},
journal= {arXiv preprint arXiv:1510.00669},
year = {2017}
}
备注
v5: reverted definition of uniform fibration to that in v3 to mirror Coquand et al., parts of development restructured accordingly; added references to some technical statements in Section 4; slightly simplified Def. 6.1; added comparison to work of Bourke/Garner (Rmk. 8.5); improved exposition and fixed various typos; 40 pages. Accepted for publication in Journal of Pure and Applied Algebra