论文标题
几乎由外侧类别中的物体决定的几乎分裂的三角形和形态
Almost Split Triangles and Morphisms Determined by Objects in Extriangulated Categories
论文作者
论文摘要
令$（\ Mathfrak {C}，\ Mathbb {e}，\ Mathfrak {s}）$为Ext-Finite，Krull-Schmidt和$ K $ -Linear-linear-linear-linear渠，$ k $ a $ k $ a a Monsuntivate artinian ring。我们定义一个加法子类别$ \ mathfrak {c} _r $（分别是$ \ mathfrak {c} _l $）的$ \ mathfrak {c} $的$ \ mathfrak {c} $，从$ \ mathfrak {c} $ modulo $ \ mathfrak的$ \ mathfrak {c} $ \ mathfrak的稳定类别中表示。 $ \ mathfrak {s} $ - projectives）至$ k $ -Modules，它由所有$ \ Mathfrak {s} $ - projective（分别分别为$ \ Mathfrak {s} $ imptive）对象和对象isomorphic isomorphic in $ \ mathfrak {s} $ - 三角形。我们研究了子类别$ \ mathfrak {c} _r $和$ \ mathfrak {c} _l $在对象确定的形态学方面，然后给出几乎拆分$ \ mathfrak {s} $ triangles的几乎分裂$ \ mathfrak {s} $。
Let $(\mathfrak{C},\mathbb{E},\mathfrak{s})$ be an Ext-finite, Krull-Schmidt and $k$-linear extriangulated category with $k$ a commutative artinian ring. We define an additive subcategory $\mathfrak{C}_r$ (respectively, $\mathfrak{C}_l$) of $\mathfrak{C}$ in terms of the representable functors from the stable category of $\mathfrak{C}$ modulo $\mathfrak{s}$-injectives (respectively, $\mathfrak{s}$-projectives) to $k$-modules, which consists of all $\mathfrak{s}$-projective (respectively, $\mathfrak{s}$-injective) objects and objects isomorphic to direct summands of finite direct sums of all third (respectively, first) terms of almost split $\mathfrak{s}$-triangles. We investigate the subcategories $\mathfrak{C}_r$ and $\mathfrak{C}_l$ in terms of morphisms determined by objects, and then give equivalent characterizations on the existence of almost split $\mathfrak{s}$-triangles.
