Recollement of colimit categories and its applications
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1147-1160
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We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and $K$-groups.
We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and $K$-groups.
DOI : 10.21136/CMJ.2020.0240-19
Classification : 18A30, 19D50
Keywords: colimit category; recollement; Leavitt path algebra; $K_i$ group
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Huang, Ju; Chen, QingHua; Lai, Chunhuan. Recollement of colimit categories and its applications. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1147-1160. doi: 10.21136/CMJ.2020.0240-19

[1] Abrams, G., Pino, G. Aranda: The Leavitt path algebra of a graph. J. Algebra 293 (2005), 319-334. | DOI | MR | JFM

[2] Hügel, L. Angeleri, Koenig, S., Liu, Q.: Recollements and tilting objects. J. Pure Appl. Algebra 215 (2011), 420-438. | DOI | MR | JFM

[3] Ara, P., Moreno, M. A., Pardo, E.: Nonstable $K$-theory for graph algebras. Algebr. Represent. Theory 10 (2007), 157-178. | DOI | MR | JFM

[4] Asadollahi, J., Hafezi, R., Vahed, R.: On the recollements of functor categories. Appl. Categ. Struct. 24 (2016), 331-371. | DOI | MR | JFM

[5] Barot, M., Lenzing, H.: One-point extensions and derived equivalence. J. Algebra 264 (2003), 1-5. | DOI | MR | JFM

[6] Beilinson, A. A., Bernstein, J., Deligne, P.: Faisceaux pervers. Analysis and Topology on Singular Spaces I Astérisque 100. Société Mathématique de France, Paris (1982), 5-171 French. | MR | JFM

[7] Bergman, G. M.: Direct limits and fixed point sets. J. Algebra 292 (2005), 592-614. | DOI | MR | JFM

[8] Chen, Q., Lin, Y.: Recollements of extension algebras. Sci. China, Ser. A 46 (2003), 530-537. | DOI | MR | JFM

[9] Cline, E., Parshall, B., Scott, L.: Algebraic stratification in representation categories. J. Algebra 117 (1988), 504-521. | DOI | MR | JFM

[10] Franjou, V., Pirashvili, T.: Comparison of abelian categories recollements. Doc. Math. 9 (2004), 41-56. | MR | JFM

[11] Fuchs, L., Göbel, R., Salce, L.: On inverse-direct systems of modules. J. Pura Appl. Algebra 214 (2010), 322-331. | DOI | MR | JFM

[12] Grothendieck, A.: Groupes de classes des categories abeliennes et triangulees. Complexes parfaits. Séminaire de Géométrie Algébrique du Bois-Marie 1965-66 SGA 5 Lecture Notes in Mathematics 589. Springer, Berlin (1977), 351-371 French. | DOI | MR | JFM

[13] Guo, X. J., Li, L. B.: $K_1$ group of finite dimensional path algebra. Acta Math. Sin., Engl. Ser. 17 (2001), 273-276. | DOI | MR | JFM

[14] Happel, D.: Reduction techniques for homological conjectures. Tsukuba J. Math. 17 (1993), 115-130. | DOI | MR | JFM

[15] Li, L. P.: Derived equivalences between triangular matrix algebras. Commun. Algebra 46 (2018), 615-628. | DOI | MR | JFM

[16] Mahmood, S. J.: Limimts and colimits in categories of d. g. near-rings. Proc. Edinb. Math. Soc., II. Ser. 23 (1980), 1-7. | DOI | MR | JFM

[17] Miyachi, J.: Localization of triangulated categories and derived categories. J. Algebras 141 (1991), 463-483. | DOI | MR | JFM

[18] Parshall, B. J., Scott, L. L.: Derived categories, quasi-hereditary algebras, and algebraic groups. Proceedings of the Ottawa-Moosonee Workshop in Algebra Mathematical Lecture Note Series. Carlton University, Ottawa (1988), 1-104. | JFM

[19] Quillen, D.: Higher algebraic $K$-theory. I. Higher $K$-Theories Lecture Notes in Mathematics 341. Springer, Berlin (1973). | DOI | MR | JFM

[20] Xue, R., Yan, Y., Chen, Q.: On colimit-categories. J. Math., Wuhan Univ. 32 (2012), 439-446. | MR | JFM

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