论文标题
离散和连续同型的合并和模型类别结构
Cofibration and Model Category Structures for Discrete and Continuous Homotopy
论文作者
论文摘要
我们表明，伪学空间和限制空间的PSTOP和LIM类别承认合并类别结构，PSTOP承认了模型类别的结构，提供了多种方法，可以同时研究经典拓扑空间的同型同质性理论，并将图形和Matroids和Matroids和Matroids和Matroids的空间组合在一起，并构成了与Sporie from confiles and corpeed and scap and scape and scaped and scale for and and nearof and nearow and and and and ofere and and ordod nearow nearow nearow。在此过程中，我们为拓扑结构提供了足够的条件，该拓扑结构包含紧凑的Hausdorff Spaces作为一个子类别，可以接纳$ i $类别结构。我们进一步表明，对于c $中的拓扑空间$ x \，在PSTOP上构建的Cofibration类别的$ X $组成的同型组对于在Top $^*$中经典构造的套件是同构的。
We show that the categories PsTop and Lim of pseudotopological spaces and limit spaces, respectively, admit cofibration category structures, and that PsTop admits a model category structure, giving several ways to simultaneously study the homotopy theory of classical topological spaces, combinatorial spaces such as graphs and matroids, and metric spaces endowed with a privileged scale, in addition to spaces of maps between them. In the process, we give a sufficient condition for a topological construct which contains compactly generated Hausdorff spaces as a subcategory to admit an $I$-category structure. We further show that, for a topological space $X\in C$, the homotopy groups of $X$ constructed in the cofibration category on PsTop are isomorphic to those constructed classically in Top$^*$.
