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2 results

  • Quillen model categories

  • Mark Hovey
  • Journal:
    Journal of K-Theory / Volume 11 / Issue 3 / June 2013
    Published online by Cambridge University Press:
    04 March 2013, pp. 469-478
    Print publication:
    June 2013

  • We provide a brief description of the mathematics that led to Daniel Quillen's introduction of model categories, a summary of his seminal work “Homotopical algebra”, and a brief description of some of the developments in the field since.

  • Classifying Spaces for Monoidal Categories Through Geometric Nerves

  • M. Bullejos, A. M. Cegarra
  • Journal:
    Canadian Mathematical Bulletin / Volume 47 / Issue 3 / 01 September 2004
    Published online by Cambridge University Press:
    20 November 2018, pp. 321-331
    Print publication:
    01 September 2004
    • Article
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  • The usual constructions of classifying spaces for monoidal categories produce $\text{CW}$-complexes with many cells that,moreover, do not have any proper geometric meaning. However, geometric nerves of monoidal categories are very handy simplicial sets whose simplices have a pleasing geometric description: they are diagrams with the shape of the 2-skeleton of oriented standard simplices. The purpose of this paper is to prove that geometric realizations of geometric nerves are classifying spaces for monoidal categories.