关于各种流形范畴中的余极限和模型结构
代数拓扑
2024-08-27 v1
摘要
在解释了模型范畴在抽象同伦论中的重要性之后，我们提供了具体例子，证明各种流形范畴并不具备所有有限余极限，因此不能成为模型范畴。然后我们考虑流形范畴的各种扩张，最终得到预层范畴。我们解释了如何在这些扩张后的范畴上产生模型结构，最终回答了涉及庞加莱空间的一个开放问题。
引用
@article{arxiv.2405.15511,
title = {On Colimits and Model Structures in Various Categories of Manifolds},
author = {David White},
journal= {arXiv preprint arXiv:2405.15511},
year = {2024}
}
备注
This paper is mostly expository but has recently generated some interest, so I am putting it on arXiv. I greatly expanded it from the version that has been on my webpage for several years, and have added the discussion of Poincare spaces