Moore流的左正则性
Left properness of Moore flows
AI总结：
该研究引入带割的重参数化范畴概念，证明此类范畴上P-空间的张量引理，进而得到P-流q-模型结构的左正则性，还证明了三类带割的重参数化范畴，其中终范畴的例子可还原普通流的对应左正则性。
AI中文摘要：
我们引入带割的重参数化范畴的概念。对每个此类重参数化范畴$\boldsymbol{\ntmathcal P}$，我们证明张量引理，即$\boldsymbol{\ntmathcal P}$-空间的两个逐对象弱同伦等价的张量积是弱等价，进而证明$\boldsymbol{\ntmathcal P}$-流的q-模型结构的左正则性。最后，我们证明区间重参数化范畴$\boldsymbol{\ntmathcal G}$、$\boldsymbol{\ntmathcal M}$以及终范畴$\boldsymbol{\nmathbf 1}$都具有割，最后这个例子可还原普通流的q-模型结构的左正则性。
英文摘要：
We introduce the notion of a reparametrization category with cuts. For every such reparametrization category $\mathcal P$, we prove the tensor lemma, namely that the tensor product of two objectwise weak homotopy equivalences of $\mathcal P$-spaces is a weak equivalence, and then the left properness of the q-model structure of $\mathcal P$-flows. Finally, we prove that the interval reparametrization categories $\mathcal G$, $\mathcal M$, as well as the final category $\mathbf 1$, have cuts. The last example recovers the left properness of the q-model structure of ordinary flows.
