一句话：基于 Awodey 的范畴神经分析，给出 Hofmann–Streicher 宇宙提升的纤维范畴相对版本。
1997 年 Hofmann 与 Streicher 给出从 Set 向 U-小范畴 B 上 Set 值预层范畴提升 Grothendieck 宇宙 U 的显式构造。Awodey 后来以范畴神经（取元素范畴函子的右伴随）作函子式分析，并指出范畴神经在 universal U-small discrete fibration 上的作用给出该提升的 generic family。受此启发，本文定义 Hofmann–Streicher 提升的相对版本：将沿纤维化 p:A→B 后复合所得的 2-函子 FibA→FibB 的右伪伴随用于构造相对提升。工作属于范畴语义/纤维化理论，摘要未报告实验评估。
In 1997, Hofmann and Streicher introduced an explicit construction to lift a Grothendieck universe ${\mathcal{U}}$ from Set into the category of Set-valued presheaves on a ${\mathcal{U}}$-small category B. More recently, Awodey presented an elegant functorial analysis of this construction in terms of the categorical nerve, the right adjoint to the functor that takes a presheaf to its category of elements; in particular, the categorical nerve's functorial action on the universal ${\mathcal{U}}$-small discrete fibration gives the generic family of ${\mathcal{U}}$'s Hofmann-Streicher lifting. Inspired by Awodey's analysis, we define a relative version of Hofmann-Streicher lifting in terms of the right pseudo-adjoint to the 2-functor FibA→ FibBgiven by postcomposition with a fibration $p:A \to B$.
DOI 原文 ·
@inproceedings{paperbot8675,
title = {Hofmann-Streicher lifting of fibred categories : Dedicated to the memory of Thomas Streicher (1958-2025)},
author = {Andrew Slattery and Jonathan Sterling},
booktitle = {LICS},
year = {2025},
doi = {10.1109/lics65433.2025.00018}
}