多点d-空间对球状复形的同伦解释
Homotopical interpretation of globular complex by multipointed d-space
摘要：
球状复合物是由E. Goubault和作者在arXiv：math/0107060中对高维自动机进行了建模。球复形是具有球分解的拓扑空间，球分解是CW-复形的胞腔分解的有向模拟。我们证明了存在一个组合模型范畴，使得细胞对象恰好是球状复合物，并且使得同伦范畴等价于arXiv：math/0308054中引入的流的同伦范畴。这个模型范畴的基础范畴是M的一个变体。Grandis关于单形生成的拓扑空间上极限上的d-空间的概念。这一结果使我们能够理解的框架之间的关系流和其他作品在有向代数拓扑使用d-空间。它还使我们能够证明，在arXiv：math/0308063中构造的流的底层同伦类型函子可以被解释为左Quillen伴随的总左导出函子，直到等价的范畴。
英文摘要：
Globular complexes were introduced by E. Goubault and the author in arXiv:math/0107060 to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CW-complex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows introduced in arXiv:math/0308054. The underlying category of this model category is a variant of M. Grandis' notion of d-space over a topological space colimit generated by simplices. This result enables us to understand the relationship between the framework of flows and other works in directed algebraic topology using d-spaces. It also enables us to prove that the underlying homotopy type functor of flows constructed in arXiv:math/0308063 can be interpreted up to equivalences of categories as the total left derived functor of a left Quillen adjoint.
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