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Cotorsion pairs in comma categories

Yuan Yuan, Jian He, Dejun Wu (2024)

Czechoslovak Mathematical Journal

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

Cuadrados especiales en la categoría de álgebras de Lie.

Daniel Tarazona (1982)

Stochastica

In this paper the concepts of mixed cartesian square and quasi-cocartesian square, already known in the category of groups, are adapted to the category of Lie algebras. These concepts can be used in the study of the obstructions of Lie algebra extensions in the same way that Wu has studied the obstructions of group extensions.

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