Geodesic
Extensions of covariantly finite subcategories revisited
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 403-415 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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).
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).
DOI : 10.21136/CMJ.2018.0338-17
Classification : 18E10, 18E30
Keywords: extriangulated category; covariantly finite subcategory 
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     title = {Extensions of covariantly finite subcategories revisited},
     journal = {Czechoslovak Mathematical Journal},
     pages = {403--415},
     year = {2019},
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     language = {en},
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He, Jing. Extensions of covariantly finite subcategories revisited. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 403-415. doi: 10.21136/CMJ.2018.0338-17

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