[Groupes d'extension inférieurs et catégories quotient]
Pour certaines sous-catégories pleines additives d'une catégorie additive , on définit les groupes d'extension inférieurs en algèbre homologique relative. Nous montrons que ces groupes sont isomorphes aux groupes Hom suspendus dans la catégorie quotient de Verdier de la catégorie homotopique bornée de par celle de . Alternativement, ces groupes sont isomorphes aux groupes de cohomologie négatifs des complexes Hom dans le dg-quotient , où et sont considérés comme dg-catégories concentrées en degré zéro.
For certain full additive subcategories of an additive category , one defines the lower extension groups in relative homological algebra. We show that these groups are isomorphic to the suspended Hom groups in the Verdier quotient category of the bounded homotopy category of by that of . Alternatively, these groups are isomorphic to the negative cohomology groups of the Hom complexes in the dg quotient category , where both and are viewed as dg categories concentrated in degree zero.
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@article{CRMATH_2019__357_11-12_832_0,
author = {Chen, Xiaofa and Chen, Xiao-Wu},
title = {The lower extension groups and quotient categories},
journal = {Comptes Rendus. Math\'ematique},
pages = {832--840},
publisher = {Elsevier},
volume = {357},
number = {11-12},
year = {2019},
doi = {10.1016/j.crma.2019.11.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.11.006/}
}
TY - JOUR AU - Chen, Xiaofa AU - Chen, Xiao-Wu TI - The lower extension groups and quotient categories JO - Comptes Rendus. Mathématique PY - 2019 SP - 832 EP - 840 VL - 357 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.11.006/ DO - 10.1016/j.crma.2019.11.006 LA - en ID - CRMATH_2019__357_11-12_832_0 ER -
%0 Journal Article %A Chen, Xiaofa %A Chen, Xiao-Wu %T The lower extension groups and quotient categories %J Comptes Rendus. Mathématique %D 2019 %P 832-840 %V 357 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.11.006/ %R 10.1016/j.crma.2019.11.006 %G en %F CRMATH_2019__357_11-12_832_0
Chen, Xiaofa; Chen, Xiao-Wu. The lower extension groups and quotient categories. Comptes Rendus. Mathématique, Tome 357 (2019) no. 11-12, pp. 832-840. doi : 10.1016/j.crma.2019.11.006. http://www.numdam.org/articles/10.1016/j.crma.2019.11.006/
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