The Grothendieck homotopy hypothesis asserts that weak infinity-groupoids model all homotopy types of spaces. In a globular formulation, cells have sources and targets in the preceding dimension, and higher cells express weak composition and invertibility. A coherator specifies the freely added operations and coherence data used to define these groupoids. Weak groupoids are essential to this formulation, which does not replace them by strict globular groupoids.
Grothendieck Homotopy Hypothesis
See also
Groupoid, Homotopy Group, Model Category, Thomason Model StructureExplore with Wolfram|Alpha
References
Henry, S. "Algebraic Models of Homotopy Types and the Homotopy Hypothesis." 15 Sep 2016. https://arxiv.org/abs/1609.04622.Cite this as:
Weisstein, Eric W. "Grothendieck Homotopy Hypothesis." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GrothendieckHomotopyHypothesis.html