Regular pairings of functors and weak (co)monads
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
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Regular pairings of functors and weak (co)monads
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| Creator |
Wisbauer, R.
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| Description |
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 A, LR defines a comonad on the category B, and there is a well-known correspondence between monads (or comonads) and adjoint pairs of functors. For various applications it was observed that the conditions for a unit of a monad was too restrictive and weakening it still allowed for a useful generalised notion of a monad. This led to the introduction of weak monads and weak comonads and the definitions needed were made without referring to this kind of adjunction. The motivation for the present paper is to show that these notions can be naturally derived from pairings of functors (L, R, α, β) with α = α ⋅ β ⋅ α and β = β ⋅ α ⋅ β. Following closely the constructions known for monads (and unital modules) and comonads (and counital comodules), we show that any weak (co)monad on A gives rise to a regular pairing between A and the category of compatible (co)modules. |
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| Date |
2019-06-09T13:38:32Z
2019-06-09T13:38:32Z 2013 |
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| Type |
Article
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| Identifier |
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.
1726-3255 2010 MSC:18A40, 18C20, 16T15. http://dspace.nbuv.gov.ua/handle/123456789/152258 |
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en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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