Weak Frobenius monads and Frobenius bimodules
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 is...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155238 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Weak Frobenius monads and Frobenius bimodules / R. Wisbauer // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 287–308. — Бібліогр.: 8 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-155238 |
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Wisbauer, R. 2019-06-16T14:26:41Z 2019-06-16T14:26:41Z 2016 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. https://nasplib.isofts.kiev.ua/handle/123456789/155238 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. The author wants to thank Bachuki Mesablishvili for proofreading. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Weak Frobenius monads and Frobenius bimodules Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Weak Frobenius monads and Frobenius bimodules |
| spellingShingle |
Weak Frobenius monads and Frobenius bimodules Wisbauer, R. |
| title_short |
Weak Frobenius monads and Frobenius bimodules |
| title_full |
Weak Frobenius monads and Frobenius bimodules |
| title_fullStr |
Weak Frobenius monads and Frobenius bimodules |
| title_full_unstemmed |
Weak Frobenius monads and Frobenius bimodules |
| title_sort |
weak frobenius monads and frobenius bimodules |
| author |
Wisbauer, R. |
| author_facet |
Wisbauer, R. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155238 |
| citation_txt |
Weak Frobenius monads and Frobenius bimodules / R. Wisbauer // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 287–308. — Бібліогр.: 8 назв. — англ. |
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2025-12-07T15:42:22Z |
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2025-12-07T15:42:22Z |
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