{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:59Z","timestamp":1740122459022,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,10,10]],"date-time":"2020-10-10T00:00:00Z","timestamp":1602288000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,10]],"date-time":"2020-10-10T00:00:00Z","timestamp":1602288000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2021,2]]},"DOI":"10.1007\/s10485-020-09609-7","type":"journal-article","created":{"date-parts":[[2020,10,10]],"date-time":"2020-10-10T08:03:43Z","timestamp":1602317023000},"page":"69-94","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Gabriel\u2013Zisman Cohomology and Spectral Sequences"],"prefix":"10.1007","volume":"29","author":[{"given":"Imma","family":"G\u00e1lvez-Carrillo","sequence":"first","affiliation":[]},{"given":"Frank","family":"Neumann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5456-5002","authenticated-orcid":false,"given":"Andrew","family":"Tonks","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,10]]},"reference":[{"key":"9609_CR1","first-page":"756","volume":"260","author":"M Andr\u00e9","year":"1965","unstructured":"Andr\u00e9, M.: Limites et fibr\u00e9s. C. R. Acad. Sci. Paris, S\u00e9r. A. 260, 756\u2013759 (1965)","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r. A."},{"key":"9609_CR2","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0022-4049(85)90008-8","volume":"38","author":"HJ Baues","year":"1985","unstructured":"Baues, H.J., Wirsching, G.: Cohomology of small categories. J. Pure Appl. Algebra 38, 187\u2013211 (1985)","journal-title":"J. Pure Appl. Algebra"},{"key":"#cr-split#-9609_CR3.1","doi-asserted-by":"crossref","unstructured":"Beilinson, A.A.: Residues and adeles. Funct. Anal. Pril. 14(1), 44-45 (1980)","DOI":"10.1007\/BF01078412"},{"key":"#cr-split#-9609_CR3.2","doi-asserted-by":"crossref","unstructured":"English transl. in: Funct. Anal. Appl. 14(1), 34-35 (1980)","DOI":"10.1007\/BF01078412"},{"key":"9609_CR4","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1090\/proc\/14679","volume":"148","author":"JE Bergner","year":"2020","unstructured":"Bergner, J.E., Osorno, A.M., Ozornova, V., Rovelli, M., Scheimbauer, C.I.: The edgewise subdivision criterion for 2-Segal objects. Proc. Am. Math. Soc. 148, 71\u201382 (2020)","journal-title":"Proc. Am. Math. Soc."},{"key":"9609_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-38117-4","volume-title":"Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics","author":"AK Bousfield","year":"1972","unstructured":"Bousfield, A.K., Kan, D.M.: Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics, vol. 304. Springer, Berlin (1972)"},{"key":"9609_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1019-1","volume-title":"Buildings","author":"KS Brown","year":"1989","unstructured":"Brown, K.S.: Buildings. Springer, Berlin (1989)"},{"key":"9609_CR7","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.jalgebra.2004.06.012","volume":"284","author":"C Ciblis","year":"2005","unstructured":"Ciblis, C., Redondo, M.J.: Cartan\u2013Leray spectral sequence for Galois coverings of linear categories. J. Algebra 284, 310\u2013325 (2005)","journal-title":"J. Algebra"},{"issue":"2","key":"9609_CR8","doi-asserted-by":"publisher","first-page":"195","DOI":"10.5802\/ambp.174","volume":"10","author":"D-C Cisinski","year":"2003","unstructured":"Cisinski, D.-C.: Images directes cohomologiques dans les cat\u00e9gories de mod\u00e8les. Ann. Math. Blaise Pascal 10(2), 195\u2013244 (2003)","journal-title":"Ann. Math. Blaise Pascal"},{"key":"9609_CR9","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/BF01389743","volume":"3","author":"A Dress","year":"1967","unstructured":"Dress, A.: Zur Spektralsequenz von Faserungen. Invent. Math. 3, 172\u2013178 (1967)","journal-title":"Invent. Math."},{"key":"9609_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-27124-4","volume-title":"Higher Segal Spaces. Lecture Notes in Mathematics","author":"T Dyckerhoff","year":"2019","unstructured":"Dyckerhoff, T., Kapranov, M.: Higher Segal Spaces. Lecture Notes in Mathematics, vol. 2244. Springer, Berlin (2019)"},{"key":"9609_CR11","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1002\/mana.19981900105","volume":"190","author":"T Fimmel","year":"1998","unstructured":"Fimmel, T.: Verdier duality for systems of coefficients over simplicial sets. Math. Nachr. 190, 51\u2013122 (1998)","journal-title":"Math. Nachr."},{"key":"9609_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-85844-4","volume-title":"Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete","author":"P Gabriel","year":"1967","unstructured":"Gabriel, P., Zisman, M.: Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 35. Springer, New York (1967)"},{"key":"9609_CR13","doi-asserted-by":"publisher","first-page":"952","DOI":"10.1016\/j.aim.2018.03.016","volume":"331","author":"I G\u00e1lvez-Carrillo","year":"2018","unstructured":"G\u00e1lvez-Carrillo, I., Kock, J., Tonks, A.: Decomposition spaces, incidence algebras and M\u00f6bius inversion I: basic theory. Adv. Math. 331, 952\u20131015 (2018)","journal-title":"Adv. Math."},{"key":"9609_CR14","doi-asserted-by":"publisher","first-page":"2549","DOI":"10.1016\/j.jpaa.2012.03.025","volume":"216","author":"I G\u00e1lvez-Carrillo","year":"2012","unstructured":"G\u00e1lvez-Carrillo, I., Neumann, F., Tonks, A.: Andr\u00e9 spectral sequences for Baues-Wirsching cohomology of categories. J. Pure Appl. Algebra 216, 2549\u20132561 (2012)","journal-title":"J. Pure Appl. Algebra"},{"key":"9609_CR15","doi-asserted-by":"publisher","first-page":"2163","DOI":"10.1016\/j.jpaa.2013.02.005","volume":"217","author":"I G\u00e1lvez-Carrillo","year":"2013","unstructured":"G\u00e1lvez-Carrillo, I., Neumann, F., Tonks, A.: Thomason cohomology of categories. J. Pure Appl. Algebra 217, 2163\u20132179 (2013)","journal-title":"J. Pure Appl. Algebra"},{"key":"9609_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12492-5","volume-title":"Methods of Homological Algebra. Springer Monographs in Mathematics","author":"SI Gelfand","year":"2003","unstructured":"Gelfand, S.I., Manin, YuI: Methods of Homological Algebra. Springer Monographs in Mathematics, 2nd edn. Springer, Berlin (2003)","edition":"2"},{"key":"9609_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8707-6","volume-title":"Simplicial Homotopy Theory, Progress in Mathematics","author":"PG Goerss","year":"1999","unstructured":"Goerss, P.G., Jardine, J.F.: Simplicial Homotopy Theory, Progress in Mathematics, vol. 174. Birkh\u00e4user Verlag, Basel (1999)"},{"key":"9609_CR18","first-page":"119","volume":"9","author":"A Grothendieck","year":"1957","unstructured":"Grothendieck, A.: Sur quelques points d\u2019alg\u00e8bre homologique. T\u00f4hoku Math. J. (2) 9, 119\u2013221 (1957)","journal-title":"T\u00f4hoku Math. J. (2)"},{"key":"9609_CR19","volume-title":"Rev\u00eatements \u00e9tales et groupe fondamental. Fasc. II: Expos\u00e9s 6, 8 \u00e0 11. S\u00e9minaire de G\u00e9om\u00e9trie Alg\u00e9brique (SGA1), 1960\/61. Troisi\u00e8me \u00e9dition, corrig\u00e9e","author":"A Grothendieck","year":"1963","unstructured":"Grothendieck, A.: Rev\u00eatements \u00e9tales et groupe fondamental. Fasc. II: Expos\u00e9s 6, 8 \u00e0 11. S\u00e9minaire de G\u00e9om\u00e9trie Alg\u00e9brique (SGA1), 1960\/61. Troisi\u00e8me \u00e9dition, corrig\u00e9e. Publications Institut des Hautes \u00c9tudes Scientifiques, Paris (1963)"},{"key":"9609_CR20","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/BF02950770","volume":"61","author":"A Huber","year":"1991","unstructured":"Huber, A.: On the Parshin\u2013Beilinson adeles for schemes. Abh. Math. Sem. Univ. Hamburg 61, 249\u2013273 (1991)","journal-title":"Abh. Math. Sem. Univ. Hamburg"},{"issue":"1","key":"9609_CR21","doi-asserted-by":"publisher","first-page":"2273","DOI":"10.1023\/A:1014945907335","volume":"110","author":"AA Husainov","year":"2002","unstructured":"Husainov, A.A.: Homological dimension theory of small categories. J. Math. Sci. 110(1), 2273\u20132321 (2002)","journal-title":"J. Math. Sci."},{"key":"9609_CR22","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s10485-018-9550-2","volume":"27","author":"AA Husainov","year":"2019","unstructured":"Husainov, A.A.: Homology groups of cubical sets. Appl. Cat. Struct. 27, 199\u2013216 (2019)","journal-title":"Appl. Cat. Struct."},{"key":"9609_CR23","volume-title":"Complexe Cotangent et D\u00e9formations II. Lecture Notes in Mathematics","author":"L Illusie","year":"1972","unstructured":"Illusie, L.: Complexe Cotangent et D\u00e9formations II. Lecture Notes in Mathematics, vol. 283. Springer, Berlin (1972)"},{"key":"9609_CR24","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/0022-4049(77)90068-8","volume":"9","author":"DM Latch","year":"1977","unstructured":"Latch, D.M.: The uniqueness of homology for the category of small categories. J. Pure Appl. Algebra 9, 221\u2013237 (1977)","journal-title":"J. Pure Appl. Algebra"},{"key":"9609_CR25","volume-title":"Categories for the Working Mathematician, Second Edition, Graduate Texts in Mathematics","author":"S MacLane","year":"1998","unstructured":"MacLane, S.: Categories for the Working Mathematician, Second Edition, Graduate Texts in Mathematics, vol. 5. Springer, New York (1998)"},{"key":"9609_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0001-8708(72)90002-3","volume":"8","author":"B Mitchell","year":"1972","unstructured":"Mitchell, B.: Rings with several objects. Adv. Math. 8, 1\u2013161 (1972)","journal-title":"Adv. Math."},{"key":"#cr-split#-9609_CR27.1","unstructured":"Parshin, A.N.: On the arithmetic of two-dimensional schemes I, repartitions and residues. Izv. Akad. Nauk SSSR Ser. Mat. 40(4), 736-773 (1976)"},{"key":"#cr-split#-9609_CR27.2","doi-asserted-by":"crossref","unstructured":"English transl. in: Math. USSR Izv. 10(4), 695-729 (1976)","DOI":"10.1070\/IM1976v010n04ABEH001810"},{"key":"9609_CR28","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s00229-006-0634-1","volume":"120","author":"T Pirashvili","year":"2006","unstructured":"Pirashvili, T., Redondo, M.J.: Cohomology of the Grothendieck construction. Manuscr. Math. 120, 151\u2013162 (2006)","journal-title":"Manuscr. Math."},{"key":"9609_CR29","doi-asserted-by":"crossref","unstructured":"Quillen, D.: Higher algebraic $$K$$-theory. I. Algebraic $$K$$-theory, I: Higher $$K$$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pp. 85\u2013147. Lecture Notes in Math. 341, Springer, Berlin (1973)","DOI":"10.1007\/BFb0067053"},{"key":"9609_CR30","doi-asserted-by":"publisher","DOI":"10.1017\/9781108855891","volume-title":"From Categories to Homotopy Theory, Cambridge Studies in Advanced Mathematics","author":"B Richter","year":"2020","unstructured":"Richter, B.: From Categories to Homotopy Theory, Cambridge Studies in Advanced Mathematics, vol. 188. Cambridge University Press, Cambridge (2020)"},{"key":"9609_CR31","first-page":"3702","volume":"252","author":"JE Roos","year":"1961","unstructured":"Roos, J.E.: Sur les foncteurs d\u00e9riv\u00e9s de $$\\lim $$. Applications. C. R. Acad. Sci. Paris, S\u00e9r. A. 252, 3702\u20133704 (1961)","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r. A."},{"key":"9609_CR32","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BF02699536","volume":"85","author":"P Schneider","year":"1997","unstructured":"Schneider, P., Stuhler, U.: Representation theory and sheaves on the Bruhat\u2013Tits building. Publ. Math. IH\u00c9S 85, 97\u2013191 (1997)","journal-title":"Publ. Math. IH\u00c9S"},{"key":"9609_CR33","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s00029-001-8098-3","volume":"7","author":"C Weibel","year":"2001","unstructured":"Weibel, C.: Homotopy ends and Thomason model categories. Selecta Mathematica, New ser. 7, 533\u2013564 (2001)","journal-title":"Selecta Mathematica, New ser."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-020-09609-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-020-09609-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-020-09609-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:14:23Z","timestamp":1633914863000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-020-09609-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,10]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["9609"],"URL":"https:\/\/doi.org\/10.1007\/s10485-020-09609-7","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"type":"print","value":"0927-2852"},{"type":"electronic","value":"1572-9095"}],"subject":[],"published":{"date-parts":[[2020,10,10]]},"assertion":[{"value":"8 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}