∞-拓扑的左正合局部化 I：高阶层
范畴论
2022-03-02 v4 代数拓扑
摘要
我们正在开发用于处理 ∞-拓扑的任意左正合局部化的工具。我们针对 ∞-拓扑 中任意一组映射 引入了高阶层(higher sheaf)的概念。我们证明高阶层全子范畴 是一个 ∞-拓扑，且层反射 是由 生成的左正合局部化。该证明依赖于同余(congruence)的概念，它是 1-拓扑理论中 Grothendieck 拓扑概念的替代。
引用
@article{arxiv.2101.02791,
title = {Left-exact Localizations of $\infty$-Topoi I: Higher Sheaves},
author = {Mathieu Anel and Georg Biedermann and Eric Finster and André Joyal},
journal= {arXiv preprint arXiv:2101.02791},
year = {2022}
}
备注
v2: 47 pages, paper substantially rewritten, proofs of main theorems shortened, examples added. v3: changed title, corrected a few typos, added Remark 3.3.10, split old Prop. 4.3.6 into new Prop. 4.3.6 and 4.3.7 for reference purposes. v4: published version, corrected typos and bibliography