发表机构
Silla University（新罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究范畴$\boldsymbol{Kur}$的基本性质，定义其纤射与弱等价以证明同伦纤维积存在，给出Weinstein范畴定义，证明$\boldsymbol{Kur}$是纤射对象范畴并讨论其同伦范畴。
AI 中文摘要
我们研究文献[Kim1]中引入的范畴$\boldsymbol{Kur}$的若干基本性质。通过定义纤射与弱等价，证明以流形为目标的态射存在同伦纤维积；该结论被用于得到两个子流形的广义相交概念。本文还给出Kuranishi空间语境下Weinstein范畴的定义，最终证明$\boldsymbol{Kur}$构成Brown[Brown]意义下的纤射对象范畴，并讨论其同伦范畴$\text{Ho}(\boldsymbol{Kur})$。
英文摘要
We study several fundamental properties of the category $\mathbf{Kur}$ introduced in \cite{Kim1}. By defining fibrations and weak equivalences, we show that morphisms with manifold targets admit homotopy fiber products; this is then applied to obtain a notion of generalized intersections of two submanifolds. A definition of the Weinstein category in the context of Kuranishi spaces is also presented. Finally, we establish that $\mathbf{Kur}$ forms a category of fibrant objects in the sense of Brown \cite{Brown}, and discuss its homotopy category $\operatorname{Ho}(\mathbf{Kur})$.
Comments88 pages
