任何理论
Theories of anything
摘要：
本文从紧李群理论的轨道范畴出发，提出了拓扑群胚π_0的一个推广，它描述了相关商对象层间的关联关系，并通过实例论证了它的实用性.本文的要点之一是Thom的结构稳定形式理论与最近由D。Spivak;另一个是Thom研究的分层与物理学中研究的相变密切相关，这里提出的π_0的推广可能在它们的研究中有用：特别是，在组织我们对自然伴随这种现象的标度律的理解方面，在凝聚态理论，生物学，金融学.
英文摘要：
We suggest a generalization of π_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of compact Lie groups. One of the points of this note is that Thom's theory of structurally stable forms fits quite nicely with the categorical theory of databases developed recently by D. Spivak; the other is that the stratifications studied by Thom are closely related to the phase transitions studied in physics, and that the generalization of π_0 proposed here may be useful in their study: in particular, in organizing our understanding of the scaling laws which naturally accompany such phenomena, in the theory of condensed matter, biology, finance ...
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
