Weak Frobenius monads and Frobenius bimodules

• Date: 2016
• Main Author: Wisbauer, Robert
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: pairing of functors; adjoint functors; weak (co)monads; Frobenius monads; firm modules; cofirm comodules; separability; 18A40; 18C20; 16T1
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/133
• Journal Title: Algebra and Discrete Mathematics

As observed by  Eilenberg and  Moore (1965), for a monad \(F\) with right adjoint comonad \(G\) on any category \(\mathbb{A}\),  the category of unital \(F\)-modules \(\mathbb{A}_F\) is isomorphic to the category of counital \(G\)-comodules \(\mathbb{A}^G\). The monad \(F\) is Frobenius provided we...