Moore流的同伦理论（I）
Homotopy theory of Moore flows (I)
AI总结：
本文修正了重参数化范畴的公理化，构造了Moore流的q-模型范畴，并证明其与流的q-模型范畴Quillen等价，为建立多基点d-空间与流之间的Quillen等价之字形迈出第一步。
摘要：
勘误，2022年7月11日：这是原论文的更新版本，原论文中重参数化范畴的概念被错误地公理化。对原论文所做更改的细节在附录中给出。重参数化范畴是一个小的拓扑富集半幺半范畴，使得半幺半结构在对象上诱导出半群结构，使得所有映射空间都是可缩的，并且使得每个映射都可以（不一定唯一地）分解为两个映射的张量积。Moore流是一个小的半范畴，它富集于重参数化范畴上的富集预层的双闭半幺半范畴之上。我们构造了Moore流的q-模型范畴。证明了它与流的q-模型范畴是Quillen等价的。这一结果是建立多基点$d$-空间的q-模型结构与流的q-模型结构之间的Quillen等价之字形的第一步。
英文摘要：
Erratum, 11 July 2022: This is an updated version of the original paper in which the notion of reparametrization category was incorrectly axiomatized. Details on the changes to the original paper are provided in the Appendix. A reparametrization category is a small topologically enriched semimonoidal category such that the semimonoidal structure induces a structure of a semigroup on objects, such that all spaces of maps are contractible and such that each map can be decomposed (not necessarily in a unique way) as a tensor product of two maps. A Moore flow is a small semicategory enriched over the biclosed semimonoidal category of enriched presheaves over a reparametrization category. We construct the q-model category of Moore flows. It is proved that it is Quillen equivalent to the q-model category of flows. This result is the first step to establish a zig-zag of Quillen equivalences between the q-model structure of multipointed $d$-spaces and the q-model structure of flows.
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