dc.contributor.author | Fløystad, Gunnar | |
dc.date.accessioned | 2024-08-07T09:15:40Z | |
dc.date.available | 2024-08-07T09:15:40Z | |
dc.date.created | 2023-06-21T10:37:30Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0927-2852 | |
dc.identifier.uri | https://hdl.handle.net/11250/3145032 | |
dc.description.abstract | We consider profunctors f : P |−→Q between posets and introduce their graph and ascent. The profunctors Pro(P, Q) form themselves a poset, and we consider a partition I F of this into a down-set I and up-set F, called a cut. To elements of F we associate their graphs, and to elements of I we associate their ascents. Our basic results is that this, suitably refined, preserves being a cut: We get a cut in the Boolean lattice of subsets of the underlying set of Q × P. Cuts in finite Booleans lattices correspond precisely to finite simplicial complexes. We apply this in commutative algebra where these give classes of Alexander dual square-free monomial ideals giving the full and natural generalized setting of isotonian ideals and letter- place ideals for posets. We study Pro(N, N). Such profunctors identify as order preserving maps f : N → N ∪ {∞}. For our applications when P and Q are infinite, we also introduce a topology on Pro(P, Q), in particular on profunctors Pro(N, N). | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Profunctors Between Posets and Alexander Duality | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2023 The Author(s) | en_US |
dc.source.articlenumber | 22 | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | 10.1007/s10485-023-09711-6 | |
dc.identifier.cristin | 2156485 | |
dc.source.journal | Applied Categorical Structures | en_US |
dc.identifier.citation | Applied Categorical Structures. 2023, 31 (2), 22. | en_US |
dc.source.volume | 31 | en_US |
dc.source.issue | 2 | en_US |