Title: Wakamatsu-tilting subcategories in extriangulated categories Show Chinese title

Title: 外延范畴中的Wakamatsu-倾斜子范畴

Abstract: Let $\mathscr{C}$ be an extriangulated category with enough projectives and injectives. We give the definitions of Wakamatsu-tilting subcategories and Wakamatsu-cotilting subcategories of $\mathscr{C}$ and show that they coincide with each other. Moreover, the definitions of $\infty$-tilting subcategories and $\infty$-cotilting subcategories given by Zhang, Wei and Wang also coincide with them. As a result, Wakamatsu-tilting subcategories success all properties of $\infty$-tilting subcategories and $\infty$-cotilting subcategories. On the other hand, we glue the Wakamatsu-tilting subcategories in a special recollement and show that the converse of the gluing holds under certain conditions. Show Chinese abstract

Abstract: 设 $\mathscr{C}$ 是一个具有足够投射对象和内射对象的外拓展范畴。 我们给出了 $\mathscr{C}$ 的 Wakamatsu-倾斜子范畴和 Wakamatsu-余倾斜子范畴的定义，并证明它们彼此一致。 此外，张、魏和王给出的 $\infty$-倾斜子范畴和 $\infty$-余倾斜子范畴的定义也与之相符。 因此，Wakamatsu-倾斜子范畴具备 $\infty$-倾斜子范畴和 $\infty$-余倾斜子范畴的所有性质。 另一方面，我们将某些特殊重合序列中的 Wakamatsu-倾斜子范畴粘合起来，并证明在一定条件下粘合的逆命题成立。