Cotorsion pairs in comma categories

Yuan Yuan; Jian He; Dejun Wu

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arXiv · 2310.15840

Cotorsion pairs in comma categories

Yuan Yuan·Jian He·Dejun Wu

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Abstract

Let A and B be abelian categories with enough projective and injective objects, and T : A-B a left exact additive functor. Then one has a comma category (B*T). It is shown that If T : A-B is X-exact, then (*X, X) is a (hereditary) cotorsion pair in A and (*Y, Y)) is a (hereditary) cotorsion pair in B if and only if ((*X, Y ), ) is a (hereditary) cotorsion pair in (B*T) and X and Y are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories A and B can induce special preenveloping classes in (B*T).

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BibTeX RIS

Yuan Yuan, Jian He, Dejun Wu. 2023-10-24. Cotorsion pairs in comma categories. https://arxiv.org/abs/2310.15840

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