Koszul complexes and relative homological algebra of functors over posets
Koszul complexes and relative homological algebra of functors over posets
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of global minimal relative resolutions. In relative homological algebra of such functors, free functors are replaced by an arbitrary family of functors. Relative Betti diagrams encode the multiplicities of these functors in minimal relative resolutions. In this article we provide conditions under which grading the chosen family of functors leads to explicit Koszul complexes whose homology dimensions are the relative Betti diagrams, thus giving a scheme for the computation of these numerical descriptors.
Chachólski, Wojciech
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Guidolin, Andrea
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Ren, Isaac
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Scolamiero, Martina
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Tombari, Francesca
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Chachólski, Wojciech
2c89303a-a3cc-45c6-9ab0-9fecd36036a0
Guidolin, Andrea
40011dc4-77ce-4d11-90bd-02e76c0b375a
Ren, Isaac
120e6485-066a-4724-b506-aec32c327b20
Scolamiero, Martina
5dd7215a-a66a-4208-a662-cf6fbf1071ff
Tombari, Francesca
69761d76-7050-4f69-b6fd-5dba13d5b468
Chachólski, Wojciech, Guidolin, Andrea, Ren, Isaac, Scolamiero, Martina and Tombari, Francesca
(2024)
Koszul complexes and relative homological algebra of functors over posets.
Foundations of Computational Mathematics.
(doi:10.1007/s10208-024-09660-z).
Abstract
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of global minimal relative resolutions. In relative homological algebra of such functors, free functors are replaced by an arbitrary family of functors. Relative Betti diagrams encode the multiplicities of these functors in minimal relative resolutions. In this article we provide conditions under which grading the chosen family of functors leads to explicit Koszul complexes whose homology dimensions are the relative Betti diagrams, thus giving a scheme for the computation of these numerical descriptors.
Text
s10208-024-09660-z
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Accepted/In Press date: 19 February 2024
e-pub ahead of print date: 18 June 2024
Identifiers
Local EPrints ID: 500904
URI: http://eprints.soton.ac.uk/id/eprint/500904
ISSN: 1615-3375
PURE UUID: 7083eabd-1772-4096-a879-95cfcb2a92ed
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Date deposited: 15 May 2025 16:59
Last modified: 02 Oct 2025 02:17
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Contributors
Author:
Wojciech Chachólski
Author:
Andrea Guidolin
Author:
Isaac Ren
Author:
Martina Scolamiero
Author:
Francesca Tombari
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