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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.\n<\/jats:p>","DOI":"10.1007\/s10208-024-09660-z","type":"journal-article","created":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T14:12:44Z","timestamp":1718719964000},"page":"1121-1165","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Koszul Complexes and Relative Homological Algebra of Functors Over Posets"],"prefix":"10.1007","volume":"25","author":[{"given":"Wojciech","family":"Chach\u00f3lski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Guidolin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Isaac","family":"Ren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martina","family":"Scolamiero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesca","family":"Tombari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"9660_CR1","unstructured":"Hideto Asashiba, Emerson\u00a0G. 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