论文标题
Abelian的信封确切类别和最高重量类别
Abelian envelopes of exact categories and highest weight categories
论文作者
论文摘要
我们在确切类别中定义了可读和弱化的子类别，并证明前者对派生类别诱导半正交分解。我们发展了薄精确类别的理论，这是由特殊集合产生的三角类别的确切类别类似物。 引入了确切类别的左右ABELIAN信封，一个示例是方案上连贯滑轮的类别，作为向量捆绑包的正确信封。右（左）abelian信封的存在被证明是针对具有弱（CO）内核的子类别的投影（内置性）生成子类别的确切类别的证明。 我们表明，最高重量类别恰恰是薄类类别的右/左信封。林吉尔二元性被解释为右与左ABELIAN信封之间的二元性。薄精确类别的二元性是通过派生类别和serre函数引入的。
We define admissible and weakly admissible subcategories in exact categories and prove that the former induce semi-orthogonal decompositions on the derived categories. We develop the theory of thin exact categories, an exact-category analogue of triangulated categories generated by exceptional collections. The right and left abelian envelopes of exact categories are introduced, an example being the category of coherent sheaves on a scheme as the right envelope of the category of vector bundles. The existence of right (left) abelian envelopes is proved for exact categories with projectively (injectively) generating subcategories with weak (co)kernels. We show that highest weight categories are precisely the right/left envelopes of thin categories. Ringel duality is interpreted as a duality between the right and left abelian envelopes of a thin exact category. The duality for thin exact categories is introduced by means of derived categories and Serre functor on them.
