发表机构
Université Libre de Bruxelles; Vrije Universiteit Brussel（布鲁塞尔自由大学; 布鲁塞尔自由大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究双（余）模与四模范畴上的辫积及预Cartier结构，分类了余代数双余模的辫积，构造了双幺半结构，并给出非零单侧预Cartier例子。
AI 中文摘要
我们研究双（余）模和四模范畴上的辫积与无穷小辫积，以及它们与双幺半结构的相容性。对于任意余代数，我们利用典范$R$-形式对其余张量积双余模范畴上的辫积进行分类，这将对偶化了Agore、Caenepeel和Militaru关于双模的分类结果。每个这样的辫积都是对称的，并且只允许零无穷小辫积。我们在辫幺半范畴中的双幺半对象上的双（余）模和四模范畴上构造双幺半结构，前提是满足关于等子与余等子的适当假设。然后我们引入预Cartier双幺半范畴及其单侧变体。我们建立了四模的相容辫积的障碍，构造了双（余）模上的非零单侧预Cartier结构，并给出了一个具有不同幺半乘积和非零无穷小辫积的预Cartier双幺半例子。
英文摘要
We study braidings and infinitesimal braidings on categories of bi(co)modules and tetramodules, and their compatibility with duoidal structures. For an arbitrary coalgebra, we classify braidings on its category of bicomodules with the cotensor product in terms of canonical $R$-forms, dualizing the classification for bimodules obtained by Agore, Caenepeel, and Militaru. Every such braiding is a symmetry and admits only the zero infinitesimal braiding. We construct duoidal structures on categories of bi(co)modules and tetramodules over bimonoids in braided monoidal categories under suitable assumptions on equalizers and coequalizers. We then introduce pre-Cartier duoidal categories and their one-sided variants. We establish obstructions to compatible braidings for tetramodules, construct nonzero one-sided pre-Cartier structures on bi(co)modules, and give a pre-Cartier duoidal example with distinct monoidal products and a nonzero infinitesimal braiding.
Comments44 pages
