{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T01:54:51Z","timestamp":1781920491313,"version":"3.54.5"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Max Planck Institute for Mathematics"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We introduce derived projective covers and explain how they are related to the notion of enough derived projectives. This provides an if-and-only-if criterion for when derived projective covers form a silting collection. We prove moreover a Koszul duality result for silting and simple-minded collections.<\/jats:p>","DOI":"10.1007\/s10485-025-09823-1","type":"journal-article","created":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T14:28:07Z","timestamp":1769956087000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Derived Projective Covers and Koszul Duality of Simple-Minded and Silting Collections"],"prefix":"10.1007","volume":"34","author":[{"given":"Lukas","family":"Bonfert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,2,1]]},"reference":[{"key":"9823_CR1","doi-asserted-by":"crossref","unstructured":"Achar, P.N.: Perverse sheaves and applications to representation theory. Mathematical Surveys and Monographs 258. American Mathematical Society, Providence, RI, (2021)","DOI":"10.1090\/surv\/258"},{"key":"9823_CR2","unstructured":"Angeleri H\u00fcgel, L., Laking, R., \u0160\u0165ov\u00ed\u010dek, J., Vit\u00f3ria, J.: Mutation and torsion pairs. Preprint. (2022). arXiv:2201.02147v1 [math.RT]"},{"issue":"3","key":"9823_CR3","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1112\/jlms\/jdr055","volume":"85","author":"T Aihara","year":"2012","unstructured":"Aihara, T., Iyama, O.: Silting mutation in triangulated categories. J. Lond. Math. Soc. (2) 85(3), 633\u2013668 (2012)","journal-title":"J. Lond. Math. Soc. (2)"},{"issue":"3","key":"9823_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1112\/plms.12176","volume":"118","author":"T Adachi","year":"2019","unstructured":"Adachi, T., Mizuno, Y., Yang, D.: Discreteness of silting objects and $$t$$-structures in triangulated categories. Proc. London Math. Soc. 118(3), 1\u201342 (2019)","journal-title":"Proc. London Math. Soc."},{"issue":"1","key":"9823_CR5","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.jpaa.2008.05.014","volume":"213","author":"S Al-Nofayee","year":"2009","unstructured":"Al-Nofayee, S.: Simple objects in the heart of a $$t$$-structure. J. Pure Appl. Algebra 213(1):54\u201359","journal-title":"J. Pure Appl. Algebra"},{"key":"9823_CR6","unstructured":"Beilinson, A., Bernstein, J., Deligne, P.: \u201cFaisceaux pervers\u201d. Ast\u00e9risque 100 (1982)"},{"issue":"2","key":"9823_CR7","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1090\/S0894-0347-96-00192-0","volume":"9","author":"A Beilinson","year":"1996","unstructured":"Beilinson, A., Ginzburg, V., Soergel, W.: Koszul duality patterns in representation theory. J. Amer. Math. Soc. 9(2), 473\u2013527 (1996)","journal-title":"J. Amer. Math. Soc."},{"issue":"1","key":"9823_CR8","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1070\/SM1991v070n01ABEH001253","volume":"70","author":"AI Bondal","year":"1991","unstructured":"Bondal, A.I., Kapranov, M.M.: Enhanced triangulated categories. Math. USSR, Sb. 70(1), 93\u2013107 (1991)","journal-title":"Math. USSR, Sb."},{"key":"9823_CR9","doi-asserted-by":"crossref","unstructured":"Bondarko, M.V.: Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields. Documenta Math, Extra Vol, 33\u2013117 (2010)","DOI":"10.4171\/dms\/5\/2"},{"key":"9823_CR10","doi-asserted-by":"crossref","unstructured":"Bondarko, M.V.: Weight structures vs.\u00a0$$t$$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general). J. $$K$$-Theory 6(3), 387\u2013504 (2010)","DOI":"10.1017\/is010012005jkt083"},{"key":"9823_CR11","unstructured":"Bondarko, M.V.: From weight structures to (orthogonal) $$t$$-structures and back. Preprint. (2019). arXiv:1907.03686v1 [math.KT]"},{"key":"9823_CR12","doi-asserted-by":"crossref","unstructured":"Br\u00fcstle, T., Yang, D.: \u201cOrdered exchange graphs\u201d. Advances in representation theory of algebras. Ed. by D.\u00a0J. Benson, H. Krause, and A. Skowro\u0144ski. EMS Series of Congress Reports. European Mathematical Society. (2014)","DOI":"10.4171\/125-1\/5"},{"key":"9823_CR13","unstructured":"Br\u00fcstle, T., Yang, D.: Ordered exchange graphs. (2023). arXiv:1302.6045v6 [math.RT]"},{"issue":"3","key":"9823_CR14","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1017\/S0305004121000086","volume":"171","author":"X-W Chen","year":"2021","unstructured":"Chen, X.-W.: Representability and autoequivalence groups. Math. Proc. Camb. Phil. Soc. 171(3), 657\u2013668 (2021)","journal-title":"Math. Proc. Camb. Phil. Soc."},{"issue":"1","key":"9823_CR15","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1112\/S0010437X21007648","volume":"158","author":"R Coelho Sim\u00f5es","year":"2022","unstructured":"Coelho Sim\u00f5es, R., Pauksztello, D., Ploog, D.: Functorially finite hearts, simple-minded systems in negative cluster categories, and noncrossing partitions. Compositio Math. 158(1), 211\u2013243 (2022)","journal-title":"Compositio Math."},{"issue":"1","key":"9823_CR16","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.indag.2021.11.004","volume":"33","author":"JN Eberhardt","year":"2022","unstructured":"Eberhardt, J.N., Stroppel, C.: Motivic Springer Theory. Indag. Math. 33(1), 190\u2013217 (2022)","journal-title":"Indag. Math."},{"key":"9823_CR17","unstructured":"Fushimi, R.: The correspondence between silting objects and $$t$$-structures for non-positive dg algebras. Preprint. (2024). arXiv:2312.17597v2 [math.RT]"},{"key":"9823_CR18","unstructured":"Fushimi, R.: Contravariant Koszul duality between non-positive and positive dg algebras. Preprint. (2025). arXiv:2409.08842v2 [math.RT]"},{"key":"9823_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2021.107826","volume":"387","author":"F Genovese","year":"2021","unstructured":"Genovese, F., Lowen, W., Van den Bergh, M.: $$t$$-structures and twisted complexes on derived injectives. Adv. Math. 387, 107826 (2021)","journal-title":"Adv. Math."},{"key":"9823_CR20","doi-asserted-by":"crossref","unstructured":"Genovese, F., Ramos Gonz\u00e1lez, J.: A derived Gabriel-Popescu theorem for t-structures via derived injectives. Int. Math. Res. Not. IMRN 2023(6), 4695\u20134760 (2023)","DOI":"10.1093\/imrn\/rnab367"},{"issue":"1","key":"9823_CR21","doi-asserted-by":"publisher","first-page":"63","DOI":"10.24033\/asens.1689","volume":"27","author":"B Keller","year":"1994","unstructured":"Keller, B.: Deriving DG categories. Ann. Sci. \u00c9c. Norm. Sup\u00e9r. (4) 27(1), 63\u2013102 (1994)","journal-title":"Ann. Sci. \u00c9c. Norm. Sup\u00e9r. (4)"},{"key":"9823_CR22","unstructured":"Keller, B., Nicol\u00e1s, P.: Notes of the talk \u201cCluster-hearts and cluster-tilting objects\u201d. Unpublished note. 2011. url: https:\/\/pnp.mathematik.uni-stuttgart.de\/iaz\/iaz1\/activities\/t-workshop\/NicolasNotes.pdf"},{"key":"9823_CR23","doi-asserted-by":"crossref","unstructured":"Keller, B., Nicol\u00e1s, P.: Weight structures and simple dg modules for positive dg algebras. Int. Math. Res. Not. IMRN 2013(5), 1028\u20131078 (2013)","DOI":"10.1093\/imrn\/rns009"},{"key":"9823_CR24","doi-asserted-by":"crossref","unstructured":"Krause, H.: Derived categories, resolutions, and Brown representability. Interactions between homotopy theory and algebra. Ed. by L.\u00a0L. Avramov, J.\u00a0D. Christensen, W.\u00a0G. Dwyer, M.\u00a0A. Mandell, and B.\u00a0E. Shipley. Contemporary Mathematics 436. (2007)","DOI":"10.1090\/conm\/436\/08405"},{"key":"9823_CR25","unstructured":"Krause, H.: Homological Theory of Representations. Cambridge Studies in Advanced Mathematics 195. Cambridge University Press, (2021)"},{"key":"9823_CR26","first-page":"239","volume":"40","author":"B Keller","year":"1988","unstructured":"Keller, B., Vossieck, D.: Aisles in derived categories. Bull. Soc. Math. Belg. 40, 239\u2013253 (1988)","journal-title":"Bull. Soc. Math. Belg."},{"key":"9823_CR27","doi-asserted-by":"publisher","first-page":"403","DOI":"10.4171\/dm\/451","volume":"19","author":"S Koenig","year":"2014","unstructured":"Koenig, S., Yang, D.: Silting objects, simple-minded collections, $$t$$-structures and co-$$t$$-structures for finite-dimensional algebras. Documenta Math. 19, 403\u2013438 (2014)","journal-title":"Documenta Math."},{"key":"9823_CR28","unstructured":"Kalck, M., Yang, D.: Relative singularity categories II: dg models. Preprint. (2018). arXiv:1803.08192v1 [math.AG]"},{"key":"9823_CR29","unstructured":"Lurie, J.: Higher Algebra. Unpublished. Sept.\u00a018, 2017. https:\/\/people.math.harvard.edu\/lurie\/papers\/HA.pdf"},{"key":"9823_CR30","unstructured":"Lurie, J.: Spectral Algebraic Geometry. Unpublished. Feb.\u00a03, 2018. https:\/\/www.math.ias.edu\/lurie\/papers\/SAG-rootfile.pdf"},{"issue":"3","key":"9823_CR31","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1090\/S0002-9947-08-04539-X","volume":"361","author":"V Mazorchuk","year":"2009","unstructured":"Mazorchuk, V., Ovsienko, S., Stroppel, C.: Quadratic duals, Koszul dual functors, and applications. Trans. Amer. Math. Soc. 361(3), 1129\u20131172 (2009)","journal-title":"Trans. Amer. Math. Soc."},{"issue":"1","key":"9823_CR32","first-page":"25","volume":"6","author":"D Pauksztello","year":"2008","unstructured":"Pauksztello, D.: Compact corigid objects in triangulated categories and co-$$t$$-structures. Centr. Eur. J. Math. 6(1), 25\u201342 (2008)","journal-title":"Centr. Eur. J. Math."},{"issue":"3","key":"9823_CR33","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1007\/s00209-017-1923-y","volume":"288","author":"C Psaroudakis","year":"2018","unstructured":"Psaroudakis, C., Vit\u00f3ria, J.: Realisation functors in tilting theory. Math. Z. 288(3), 965\u20131028 (2018)","journal-title":"Math. Z."},{"key":"9823_CR34","doi-asserted-by":"crossref","unstructured":"Rickard, J.: Equivalences of derived categories for symmetric algebras. J. Algebra 257(2), 460\u2013481 (2002)","DOI":"10.1016\/S0021-8693(02)00520-3"},{"key":"9823_CR35","unstructured":"Schn\u00fcrer, O.M.: Simple-minded subcategories and $$t$$-structures. Unpublished note. 2020. https:\/\/math.uni-paderborn.de\/fileadmin-eim\/mathematik\/AG-Algebra\/Notes\/simple-minded-subcategories-and-t-structures.pdf"},{"key":"9823_CR36","unstructured":"The Stacks Project Authors. Stacks Project. https:\/\/stacks.math.columbia.edu. (2018)"},{"key":"9823_CR37","doi-asserted-by":"crossref","unstructured":"Su, H., Yang, D.: From simple-minded collections to silting collections via Koszul duality. Algebr. Represent. Theor. 22, 219\u2013238 (2019)","DOI":"10.1007\/s10468-018-9763-y"},{"issue":"11","key":"9823_CR38","doi-asserted-by":"publisher","first-page":"4815","DOI":"10.1080\/00927872.2023.2217449","volume":"51","author":"H Zhang","year":"2023","unstructured":"Zhang, H.: The ST correspondence for proper non-positive dg algebras. Comm. Algebra 51(11), 4815\u20134820 (2023)","journal-title":"Comm. Algebra"}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-025-09823-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-025-09823-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-025-09823-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T17:29:51Z","timestamp":1781630991000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-025-09823-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,1]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["9823"],"URL":"https:\/\/doi.org\/10.1007\/s10485-025-09823-1","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"value":"0927-2852","type":"print"},{"value":"1572-9095","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,1]]},"assertion":[{"value":"20 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"10"}}