论文标题
免费分解空间
Free decomposition spaces
论文作者
论文摘要
我们介绍了自由分解空间的概念：它们是由其惰性地图自由产生的简单空间。我们表明，沿包含$ j \colonδ_ {\ operatotorName {intert}} \δ$的左KAN扩展将一般对象带到Möbius分解空间，并将一般地图与Culf Maps相关。我们建立了$ \ infty $ -CATEGIORY $ \ MATHBF {prsh}（δ_ {\ propatatorName {inert}}）\ simeq \ simeq \ simeq \ mathbf {decomp} _ {/b \ mathbb {n}} $。尽管免费的分解空间是相当简单的对象，但它们中的组合学丰富：似乎所有脱谐型类型的合并均来自自由分解空间。我们提供了广泛的示例列表，包括准对称函数。
We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon Δ_{\operatorname{inert}} \to Δ$ takes general objects to Möbius decomposition spaces and general maps to CULF maps. We establish an equivalence of $\infty$-categories $\mathbf{PrSh}(Δ_{\operatorname{inert}}) \simeq \mathbf{Decomp}_{/B\mathbb{N}}$. Although free decomposition spaces are rather simple objects, they abound in combinatorics: it seems that all comultiplications of deconcatenation type arise from free decomposition spaces. We give an extensive list of examples, including quasi-symmetric functions.
