Dwyer 映射的推出是 $(\infty,1)$-范畴性的
代数拓扑
2024-07-24 v3 范畴论
摘要
1-范畴到 -范畴的嵌入一般不能保持余极限，尤其是推出。在本注记中，我们观察到若范畴跨中的某个函子属于先前已识别的某类函子，则该 1-范畴推出在此嵌入下得以保持。Dwyer 映射——一种范畴的邻域形变收缩——曾被 Thomason 用于构造其 1-范畴上的模型结构。Thomason 先前观察到此类推出的神经具有正确的弱同伦型。我们精炼该结果并证明此弱同伦等价是一个弱范畴等价。我们还识别出一类更一般的函子，沿其 1-范畴推出是 -范畴性的。
引用
@article{arxiv.2205.02353,
title = {Pushouts of Dwyer maps are $(\infty,1)$-categorical},
author = {Philip Hackney and Viktoriya Ozornova and Emily Riehl and Martina Rovelli},
journal= {arXiv preprint arXiv:2205.02353},
year = {2024}
}
备注
v3: Major rewrite based on an alternate proof strategy proposed by a referee that uses a different model of $\infty$-categories. 12 pages. Prior proof may be found in v2. v2: Minor clarifications and corrections suggested by a referee. v1: An expansion and correction of a result from arxiv:2106.03660v2