Homotopical realizations of innity groupoids

• Jan McGarry Furriol ^[1]
  1. [1] University of Copenhagen

     University of Copenhagen

     Dinamarca

     
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 6, Nº. 1, 2021, págs. 49-57
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • català

    La hipòtesi d’homotopia de Grothendieck afirma que l’estudi dels tipus d’homotopia dels espais topològics és equivalent a l’estudi dels ∞-grupoides. En la pràctica, un cop triat un model per a les categories d’ordre superior, l’equivalència és realitzada per l’assignació del ∞-grupoide fonamental a un espai topològic. Proposem un model accessible per al ∞-grupoide fonamental, usant categories topològiques per a modelitzar els ∞-grupoides.

  • English

    Grothendieck’s homotopy hypothesis asserts that the study of homotopy types of topological spaces is equivalent to the study of ∞-groupoids. In practice, after one has chosen a model for higher categories, the equivalence is realized by the assignment of the fundamental ∞-groupoid to a topological space. We propose an accessible model for the fundamental ∞-groupoid, using topological categories to model ∞-groupoids.

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