Czechoslovak Mathematical Journal, Vol. 69, No. 2, pp. 403-415, 2019
Extensions of covariantly finite subcategories revisited
Received July 22, 2017. Published online August 24, 2018.
Abstract: Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of homotopy cartesian square in an extriangulated category is defined in this article. We prove that in an extriangulated category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. As an application, we give a simultaneous generalization of a result of X. W. Chen (2009) and of a result of R. Gentle, G. Todorov (1996).
Affiliations: Jing He, College of Mathematics and Statistics, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Mulanlou, 36 Lushan Rd., Yuelu District, Changsha, Hunan 410081, P. R. China, e-mail: email@example.com