Regular pairings of functors and weak (co)monads

• Published in: Algebra and Discrete Mathematics
• Date: 2013
• Main Author: Wisbauer, R.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/152258
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Regular pairings of functors and weak (co)monads / R. Wisbauer // Algebra and Discrete Mathematics. — 2013. — Vol. 15, № 1. — С. 127–154. — Бібліогр.: 23 назв. — англ.

For functors L : A → B and R : B → A between any categories A and B, a pairing is defined by maps, natural in A ∈ A and B ∈ B,
 MorB(L(A), B) ↔ MorA(A, R(B)).
 (L, R) is an adjoint pair provided α (or β) is a bijection. In this case the composition RL defines a monad on the category...