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Kuranishi spaces in a category of fibrant objects and their homotopy fiber products
Abstract
We study several fundamental properties of the category 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 Kur forms a category of fibrant objects in the sense of Brown \cite{Brown}, and discuss its homotopy category Ho(Kur).
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BibTeX
@misc{kim2026kuranishi,
title = {{Kuranishi spaces in a category of fibrant objects and their homotopy fiber products}},
author = {Taesu Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11594},
eprint = {2610.11594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11594},
}
RIS
TY - UNPB
TI - Kuranishi spaces in a category of fibrant objects and their homotopy fiber products
AU - Taesu Kim
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11594
UR - https://arxiv.org/abs/2610.11594
AB - We study several fundamental properties of the category 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 Kur forms a category of fibrant objects in the sense of Brown \cite{Brown}, and discuss its homotopy category Ho(Kur).
ER -