Erratum to "Homotopy theory of Moore flows I"

Homotopy theory of Moore flows (II)

This paper proves that the q-model structures of Moore flows and of multipointed $d$-spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed $d$-spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a …

Note on the tensor product of dendroidal sets

In our paper "Dendroidal sets as models for homotopy operads" (J. Topol. 4 (2011), no. 2, 257-299, and arXiv:0902.1954), we made the wrong claim about the behaviour of the tensor product with respect to cofibrations of dendroidal sets. We added an erratum at the end of the arXiv version of loc. cit. This short note contains the proof of a technical lemma used in the erratum.

Moore流的同伦理论（I）

Homotopy theory of Moore flows (I)

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。

Torsion theories of simplicial groups with truncated Moore complex

We introduce a linearly ordered lattice $μ(Grp)$ of torsion theories in simplicial groups. The torsion theories are defined where the torsion/torsion-free subcategories are given by the simplicial groups with bounded above/below Moore complex, respectively. These torsion theories extend naturally the torsion theories in internal groupoids in groups. Connections of this lattice with the homotopy groups are established since the homotopy groups of a simplicial group can be calculated as the quotients of torsion subojects.

Homotopy theory of Moore flows (III)

The previous paper of this series shows that the q-model categories of $\mathcal{G}$-multipointed $d$-spaces and of $\mathcal{G}$-flows are Quillen equivalent. In this paper, the same result is established by replacing the reparametrization category $\mathcal{G}$ by the reparametrization category $\mathcal{M}$. Unlike the case of $\mathcal{G}$, the execution paths of a cellular $\mathcal{M}$-multipointed $d$-space can have stop intervals. The technical tool to overcome this obstacle is the notion of globular naturalization. It is the globular analogue of Raussen's naturalization of a directed …

Moore流的左正则性

Left properness of Moore flows

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。