Regular pairings of functors and weak (co)monads

• Date: 2018
• Main Author: Wisbauer, Robert
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: pairing of functors; adjoint functors; weak monads and comonads; \(r\)-unital monads; \(r\)-counital comonads; 18A40; 18C20; 16T15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/738
• Journal Title: Algebra and Discrete Mathematics

For functors \(L:\mathbb{A}\to \mathbb{B}\) and \(R:\mathbb{B}\to \mathbb{A}\) betweenany categories \(\mathbb{A}\) and \(\mathbb{B}\), a  pairing is defined by maps, natural in \(A\in \mathbb{A}\) and  \(B\in \mathbb{B}\),\[\xymatrix{{\rm Mor}_\mathbb{B} (L(A),B) \ar@<0.5ex>[r]^{\alph...