一句话：证明单值富集范畴间本质满且完全忠实的函子是等价，并构造富集 Rezk 完备化及单值富集 Kleisli 范畴。
富集范畴的态射集带有额外结构，在高阶范畴、同伦论与程序语言语义中具有重要作用。本文研究单值（univalent）富集范畴：首先证明此类范畴之间本质满且完全忠实的函子必为等价，从而给出单值性在富集情形下的等价刻画；随后证明每个富集范畴都可构造 Rezk 完备化，即一种保持等价的自由单值化构造。最后，作者利用富集范畴的 Rezk 完备化构造单值富集 Kleisli 范畴，展示该构造在单子与计算语义中的应用。
Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this paper, we study univalent enriched categories. We prove that all essentially surjective and fully faithful functors between univalent enriched categories are equivalences, and we show that every enriched category admits a Rezk completion. Finally, we use the Rezk completion for enriched categories to construct univalent enriched Kleisli categories.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{Weide24,
title = {Univalent Enriched Categories and the Enriched Rezk Completion},
author = {Niels van der Weide},
journal = {Logical Methods in Computer Science},
volume = {Volume 22, Issue 2},
year = {2026},
doi = {10.46298/lmcs-22(2:25)2026}
}