Year: 2026
Type: preprint
Abstract: 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 $\operatorname{Ho}(\mathbf{Kur})$.
Source: arXiv (Cornell University)
Author: Kim, Taesu
Institution: Silla University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221134654