Weak Frobenius monads and Frobenius bimodules
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
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Weak Frobenius monads and Frobenius bimodules
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| Creator |
Wisbauer, R.
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| Description |
As observed by Eilenberg and Moore (1965), for a monad F with right adjoint comonad G on any category A, the category of unital F-modules AF is isomorphic to the category of counital G-comodules AG. The monad F is Frobenius provided we have F=G and then AF≃AF. Here we investigate which kind of isomorphisms can be obtained for non-unital monads and non-counital comonads. For this we observe that the mentioned isomorphism is in fact an isomorphisms between AF and the category of bimodules AFF subject to certain compatibility conditions (Frobenius bimodules). Eventually we obtain that for a weak monad (F,m,η) and a weak comonad (F,δ,ε) satisfying Fm⋅δF=δ⋅m=mF⋅Fδ and m⋅Fη=Fε⋅δ, the category of compatible F-modules is isomorphic to the category of compatible Frobenius bimodules and the category of compatible F-comodules.
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| Date |
2019-06-16T14:26:41Z
2019-06-16T14:26:41Z 2016 |
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| Type |
Article
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| Identifier |
Weak Frobenius monads and Frobenius bimodules / R. Wisbauer // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 287–308. — Бібліогр.: 8 назв. — англ.
1726-3255 2010 MSC:18A40, 18C20, 16T1. http://dspace.nbuv.gov.ua/handle/123456789/155238 |
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| Language |
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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