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Simplicial sets are discrete, combinatorial models for topological spaces that simplify the construction of many objects in topology. It turns out that the homotopy theory of simplicial sets is equivalent to that of topological spaces. The importance of simplicial sets for topology is based on the fact that many objects in topology are constructed as realisations of simplicial sets. Some perspectives on this will be given at the end of this chapter.

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Simplicial Sets

  • 章节

  • 发表日期：

    2025年

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  • Gerd Laures,
  • Markus Szymik

摘要

Simplicial sets are discrete, combinatorial models for topological spaces that simplify the construction of many objects in topology. It turns out that the homotopy theory of simplicial sets is equivalent to that of topological spaces. The importance of simplicial sets for topology is based on the fact that many objects in topology are constructed as realisations of simplicial sets. Some perspectives on this will be given at the end of this chapter.