Abstract
We study t-structures generated by sets of objects which satisfy a condition weaker than the compactness. We also study weight structures cogenerated by sets of objects satisfying the dual condition. Under some appropriate hypothesis, it turns out that the weight structure is right adjacent to the t-structure.
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Angeleri Hügel, L.: Silting objects. Bull. Lond. Math. Soc. 51(4), 658–690 (2019). https://doi.org/10.1112/blms.12264
Beilinson, A., Bernstein, J., Deligne, P.: Faisceaux Pervers. In: Analysis and Topology on Singular Spaces. Societe Mathematique de France, Paris, Asterisque 100, 5–171 (1982)
Beligiannis, A.: Relative homological algebra and purity in triangulated categories. J. Algebra 227, 268–361 (2000)
Bondarko, M.: Weight structures vs. t-structures, weight filtrations, spectral sequences, and complexes (for motives and in general). J. K-Theory 6, 387–504 (2010)
Bondarko, M.: On perfectly generated weight structures and adjacent t-structures. Math. Z. 300(2022) , 1421–1454. https://doi.org/10.1007/s00209-021-02815-6
Keller, B., Nicolás, P.: Weight structures and simple dg modules for positive dg algebras. Int. Math. Res. Not. 2013, 1028–1078 (2013)
Krause, H.: On Neeman’s well generated triangulated categories. Documenta Math. 6, 121–126 (2001)
Krause, H.: A Brown representability theorem via coherent functors. Topology 41, 853–861 (2002)
Marks, F., Vitória, J.: Silting and cosilting classes in derived categories. J. Algebra 501, 526–544 (2018)
Modoi, G.C.: On perfectly generating projective classes in triangulated categories. Commun. Algebra 38, 995–1011 (2010)
Modoi, G.C.: The dual of Brown representability for homotopy categories of complexes. J. Algebra 392, 115–124 (2013)
Modoi, G.C.: The dual of the homotopy category of projective modules satisfies Brown representability. B. Lond. Math. Soc. 46, 765–770 (2014)
Modoi, G.C.: Constructing cogenerators in triangulated categories and Brown representability. J. Pure Appl. Algebra 219(8), 3214–3224 (2015)
Modoi, G.C.: The dual of Brown representability for some derived categories. Ark. Math. 54, 485–498 (2016)
Neeman, A.: Triangulated Categories. Annals of Mathematics Studies, vol. 148. Princeton University Press, Princeton, NJ (2001)
Neeman, A.: The homotopy category of flat modules, and Grothendieck duality. Invent. Math. 174, 255–308 (2008)
Neeman, A.: Brown Representability follows from Rosický’s theorem. J. Topol. 2, 262–276 (2009)
Neeman, A.: Some adjoints in homotopy categories. Ann. Math. 171, 2143–2155 (2010)
Neeman, A.: Explicit cogenerators for the homotopy category of projective modules over a ring. Ann. Sci. Ec. Norm. Sup. 44, 607–629 (2011)
Oppermann, S., Psaroudakis, C., Stai, T.: Change of rings and singularity categories. Adv. Math. 350, 190–241 (2019)
Pauksztello, D.: Compact cochain objects in triangulated categories and co-t-structures. Central Eur. J. Math. 6, 25–42 (2008)
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The author would like to thank to an anonymous referee for many suggestions which strongly improved the presentation of this paper.
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Communicated by Henning Krause.
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Modoi, G.C. Weight Structures Cogenerated by Weak Cocompact Objects. Appl Categor Struct 30, 921–936 (2022). https://doi.org/10.1007/s10485-022-09676-y
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DOI: https://doi.org/10.1007/s10485-022-09676-y