Simplicial stuff

Inspired by the MO tag , “simplicial stuff” refers to simplicial sets , simplicial objects in a category, geometric realization, and related topics.

Literature

General

  • Riehl, 2008, lecture notes: A leisurely introduction to simplicial sets (pdf)
  • Friedman, 2012: Survey article: An elementary illustrated introduction to simplicial sets (doi, arxiv)
    • An excellent first introduction to simplicial sets and semi-simplicial sets
  • Singh, 2018, MSc thesis: A survey of simplicial sets (pdf)
  • Robinson et al, 2018: Local homology of abstract simplicial complexes (arxiv)
    • Survey of local homology of graphs and of higher-dimensional abstract simplicial complexes
    • Sec. 3 opens with exposition of Alexandrov topology
  • Hosgood, 2021: Various notions of (co)simplicial (pre)sheaves (arxiv)

Symmetric simplicial sets (aka symmetric sets )

  • Grandis, 2001: Finite sets and symmetric simplicial sets (pdf)
    • A standard reference for symmetric sets
    • Sequel paper: Grandis, 2001: Higher fundamental functors for simplicial sets (arxiv, pdf)
  • Antokoletz, 2010: An alternative presentation of the symmetric-simplicial category (arxiv)

Applied simplicial stuff

  • Greening, Pinter-Wollman, Fefferman, 2015: Higher-order interactions: Understanding the knowledge capacity of social groups using simplicial sets (doi)
  • Spivak, 2009: Higher-dimensional models of networks (arxiv)
    • Functors between graphs, hypergraphs, semi-simplicial sets, and simplicial sets, motivated by mathematical modeling of networks
  • Spivak, 2009: Simplicial databases (arxiv)
    • Spivak, 2010: Table manipulation in simplicial databases (arxiv)
    • Precursor to functorial data migration