无环映射的一些特征

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2019-03-04 DOI:10.1007/s40062-019-00231-6

George Raptis

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引用次数: 13

摘要

讨论了空间间无环映射类的两个范畴刻画。第一个是关于上属论的更高范畴概念。第二个使用了平衡映射的概念，也就是说，一个映射的同伦回拉沿着\(\pi _0\) -满射映射也定义了同伦推拉。我们还在空间同伦理论中识别了由无环映射类定义的模态，并讨论了该模态的广义Blakers-Massey定理的内容。

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Some characterizations of acyclic maps

We discuss two categorical characterizations of the class of acyclic maps between spaces. The first one is in terms of the higher categorical notion of an epimorphism. The second one employs the notion of a balanced map, that is, a map whose homotopy pullbacks along \(\pi _0\)-surjective maps define also homotopy pushouts. We also identify the modality in the homotopy theory of spaces that is defined by the class of acyclic maps, and discuss the content of the generalized Blakers–Massey theorem for this modality.

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.