一句话：证明 (T,V)-范畴上的预层单子是 simple 的，由此构造松弛正交因子分解系统，其弱系统左部为 embeddings。
本文研究在 quantale V 与 Set-单子 T 松弛扩展到 V-Rel 的设定下，如何构造弱因子分解系统。作者考察 (T,V)-范畴上的预层单子，证明该单子是 simple 的，从而得到松弛正交因子分解系统（LOFS），并说明其对应的弱因子分解系统的左部由 embeddings 构成。文章还引入预层子单子，研究它们定义的 LOFS，给出从单子与 quantale 数据构造 LOFS 的一般方法。作为应用，该方法可在若干 Set 上已知拓扑范畴的例子中构造弱因子分解系统。
We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$ laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of $(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose corresponding weak factorisation system has embeddings as left part. In addition, we present presheaf submonads and study the LOFSs they define. This provides a method of constructing weak factorisation systems on some well-known examples of topological categories over $\mathsf{Set}$.Comment: 13 pages. Minor changes from previous version
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{ClementinoF17,
title = {Lax orthogonal factorisations in monad-quantale-enriched categories},
author = {Maria Manuel Clementino and Ignacio Lopez Franco},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:32)2017}
}