Extensions of covariantly finite subcategories revisited

Jing He

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 2, page 403-415
  • ISSN: 0011-4642

Abstract

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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).

How to cite

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He, Jing. "Extensions of covariantly finite subcategories revisited." Czechoslovak Mathematical Journal 69.2 (2019): 403-415. <http://eudml.org/doc/294451>.

@article{He2019,
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).},
author = {He, Jing},
journal = {Czechoslovak Mathematical Journal},
keywords = {extriangulated category; covariantly finite subcategory},
language = {eng},
number = {2},
pages = {403-415},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extensions of covariantly finite subcategories revisited},
url = {http://eudml.org/doc/294451},
volume = {69},
year = {2019},
}

TY - JOUR
AU - He, Jing
TI - Extensions of covariantly finite subcategories revisited
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 403
EP - 415
AB - 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).
LA - eng
KW - extriangulated category; covariantly finite subcategory
UR - http://eudml.org/doc/294451
ER -

References

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  11. Nakaoka, H., Palu, Y., Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories, Available at https://arxiv.org/abs/1605.05607v2. 
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