论文标题
在精确且弱精确的结构的晶格上
On the lattices of exact and weakly exact structures
论文作者
论文摘要
我们在本文中启动了弱精确结构的研究，这是quillen精确结构的概括。我们引入了单面精确结构的弱对应物，并表明左和右弱确切结构会产生弱精确的结构。我们进一步在加性类别$ \ Mathcal {a} $上定义了弱外侧的结构，并表征了它们之间弱精确的结构。 我们调查了$ \ Mathcal {a} $ form lattices上的这些结构何时。我们证明，弱外侧结构的子结构的晶格与某个函子类别的子类别的晶格是同构的。在能完成的情况下，我们表征了所有弱精确结构的晶格，并证明存在独特的最大弱精确结构。 我们详细研究了$ \ Mathcal {a} $具有添加性有限的情况，从而给出了所有附加子插件的$ \ mbox {ext}^1 $的封闭子界面的模块理论表征。
We initiate in this article the study of weakly exact structures, a generalization of Quillen exact structures. We introduce weak counterparts of one-sided exact structures and show that a left and a right weakly exact structure generate a weakly exact structure. We further define weakly extriangulated structures on an additive category $\mathcal{A}$ and characterize weakly exact structures among them. We investigate when these structures on $\mathcal{A}$ form lattices. We prove that the lattice of substructures of a weakly extriangulated structure is isomorphic to the lattice of topologizing subcategories of a certain functor category. In the idempotent complete case, we characterize the lattice of all weakly exact structures and we prove the existence of a unique maximal weakly exact structure. We study in detail the situation when $\mathcal{A}$ is additively finite, giving a module-theoretic characterization of closed sub-bifunctors of $\mbox{Ext}^1$ among all additive sub-bifunctors.
