Recommender systems build user profiles using concept analysis of usage matrices. The concepts are mined as spectra and form Galois connections. Descent is a general method for spectral decomposition in algebraic geometry and topology which also leads to generalized Galois connections. Both recommender systems and descent theory are vast research areas, separated by a technical gap so large that trying to establish a link would seem foolish. Yet a formal link emerged, all on its own, bottom-up, against authors' intentions and better judgment. Familiar problems of data analysis led to a novel solution in category theory. The present paper arose from a series of earlier efforts to provide a top-down account of these developments.

翻译：推荐系统通过使用矩阵的概念分析构建用户画像。这些概念作为谱被挖掘出来，并构成伽罗瓦连接。下降是代数几何与拓扑中一种通用的谱分解方法，它同样引出了广义的伽罗瓦连接。推荐系统与下降理论均为广阔的研究领域，二者之间横亘着巨大的技术鸿沟，试图建立联系看似愚蠢。然而，一个形式上的联系却自发地、自下而上地浮现了，这违背了作者的初衷与更优的判断。数据分析领域的常见问题催生了范畴论中的一个新颖解决方案。本文源自一系列早期尝试，旨在自上而下地阐述这些发展。