∞- operad 族与 ∞-operadic Kan 扩张的幺半包络
范畴论
2025-07-22 v2 代数拓扑
摘要
我们给出 Lurie 关于 operadic Kan 扩张定理证明的细节。在此过程中，我们将 ∞-operad 的幺半包络构造推广到 ∞-operad 族，并用它构造纤维直和函子，二者皆由某些泛性质刻画。除在 Lurie 定理证明中的用途外，这些结果与构造本身也具有独立意义。
引用
@article{arxiv.2303.10813,
title = {Monoidal Envelopes of Families of $\infty$-Operads and $\infty$-Operadic Kan Extensions},
author = {Kensuke Arakawa},
journal= {arXiv preprint arXiv:2303.10813},
year = {2025}
}
备注
Major revision. Proof of 1.1 simplified (now 2.1). Clarified relation to HA (Section 1). Gave a satisfactory universal property of monoidal envelopes of families (3.5). Improved exposition. 32 pages, identical to the version accepted in Applied Categorical Structures except for formatting