DC Field | Value | Language |
---|---|---|
dc.contributor.author | Femić, Bojana | en_US |
dc.date.accessioned | 2022-04-26T09:57:35Z | - |
dc.date.available | 2022-04-26T09:57:35Z | - |
dc.date.issued | 2022-01-01 | - |
dc.identifier.issn | 0219-4988 | - |
dc.identifier.uri | http://researchrepository.mi.sanu.ac.rs/handle/123456789/4777 | - |
dc.description.abstract | We characterize in bicategorical terms actions of monoidal categories on the categories of representations of algebras and of relative Hopf modules. For this purpose we introduce 2-cocycles in any 2-category . We observe that under certain conditions the structures of pseudofunctors between bicategories are in one-to-one correspondence with (twisted) 2-cocycles in the image bicategory. In particular, for certain pseudofunctors to Cat, the 2-category of categories, one gets 2-cocycles in the free completion 2-category under Eilenberg-Moore objects, constructed by Lack and Street. We introduce (co)quasi-bimonads in and a suitable bicategory of Tambara (co)modules over (co)quasi-bimonads in fitting the setting of the latter pseudofuntors. We describe explicitly the involved 2-cocycles in this context and show how they are related to Sweedler's and Hausser-Nill 2-cocycles in , which we define. This allows us to recover some results of Schauenburg, Balan, Hausser and Nill for modules over commutative rings. We fit a version of the 2-category of bimonads in , which we introduced in a previous paper, in a similar setting as above and recover a result of Laugwitz. We observe that pseudofunctors to Cat in general determine what we call pseudo-actions of hom-categories, which correspond to the whole range of a 2-cocycle, so that the described actions of categories appear as restrictions of these 2-cocycles to endo-hom categories. | en_US |
dc.publisher | World Scientific | en_US |
dc.relation.ispartof | Journal of Algebra and its Applications | en_US |
dc.subject | 2-(co)monads | action of categories | bicategories | Monoidal categories | quasi-bialgebras | Yetter-Drinfel'd modules | en_US |
dc.title | A bicategorical approach to actions of monoidal categories | en_US |
dc.type | Article | en_US |
dc.identifier.doi | 10.1142/S0219498823500731 | - |
dc.identifier.scopus | 2-s2.0-85123921252 | - |
dc.contributor.affiliation | Mathematics | en_US |
dc.contributor.affiliation | Mathematical Institute of the Serbian Academy of Sciences and Arts | - |
dc.relation.firstpage | 2350073 | - |
dc.description.rank | ~M23 | - |
item.grantfulltext | none | - |
item.cerifentitytype | Publications | - |
item.fulltext | No Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | Article | - |
crisitem.author.dept | Mathematical Institute of the Serbian Academy of Sciences and Arts | - |
crisitem.author.orcid | 0000-0002-5767-1708 | - |
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