Exactness of direct limits for abelian categories with an injective cogenerator
نویسندگان
چکیده
منابع مشابه
Semi-abelian Categories and Exactness
We show that every semi-abelian category, as defined by Palamodov, possesses a maximal exact structure in the sense of Quillen and that the exact structure of a quasi-abelian category is a special case thereof.
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THEOREM I. Let X be a small category. Then the following assertions are equivalent: (1) The inverse limit proj limx: AB-^AB is exact (2) For every abelian category SÏ with exact direct products y the inverse limit proj lim* : %—»3I is exact. (3) Every connected component Y of X contains an object y together with an endomorphism eÇz Y (y, y) such that the following properties are satisfied: (i) ...
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چکیده ندارد.
Gorenstein projective objects in Abelian categories
Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2019
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2018.11.004