T.T.F. theories in abelian categories
T.T.F. theories in abelian categories
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DOI：
10.1080/00927878808823609
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发表时间：
1988
影响因子：
0.7
通讯作者：
R. Gentle
中科院分区：
文献类型：
--
作者：
R. Gentle
给定（T，S，R），在具有充分投射和内射对象的阿贝尔范畴A中的Torsion-Torsion Free（T.T.F）理论。证明了全子范畴T与R的交是关于Serre子范畴S的可加分式范畴，R <$T是阿贝尔范畴。R的投射对象的子范畴与A在T中的投射对象的子范畴之间建立了等价关系。对于内射对象也有类似的等价。若T有一个小投射对象的生成集，则证明了R有一个不可分解的内射的余生成集。
Given (T,S,R), a Torsion-Torsion Free (T.T.F) theory in an abeiian category A with sufficient projective and injective objects. it is shown that the intersection of the full subcategories T and R is the additive category of fractions with respect to the Serre subcategory S, R ⋂ T is an abelian category. An equivalence is established between the subcategories of the projective objects of R ⋂ T and the projective objects of A in T. There is also a similar equivalence for injective objects. If T has a generating set of small projective objects, it is shown that R has a cogenerating set of indecomposable injectives.