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1 results

  • 14 - Higher Categories

  • from Part IV - Polygraphs
  • Dimitri Ara, Aix-Marseille Université, Albert Burroni, Université Paris Cité, Yves Guiraud, Université Paris Cité, Philippe Malbos, Université Claude Bernard Lyon 1, François Métayer, Université Paris Cité, Samuel Mimram, École Polytechnique, Paris
  • Book:
    Polygraphs: From Rewriting to Higher Categories
    Published online:
    18 March 2025
    Print publication:
    03 April 2025, pp 299-315

  • Summary

    Among the many existing notions of higher categories, the notion of strict globular n-category is, in some sense, the most basic one. In this chapter, the essential definitions and notations are set. Starting with a description of the basic "shapes", that is, the presheaf category of globular sets, family of operations endowing a globular set with a structure of ω-category is defined. Then, it is proven that the category of strict ω-categories is exactly the category of algebras of the monad induced by the forgetful functor from ω-categories to globular sets. Finally, important subcategories of ω-categories, obtained by requiring cells to be invertible above a given dimension, are defined.