Edoardo Lanari (Macquarie University), Globular models for weak higher dimensional structures



The state of the art of higher category theory offers a wide variety of models for ∞-categories, and introduces the problem of comparing them. The two most important differences consist of the basic shapes we allow for our theory and their being algebraic or not. We will introduce a globular model for ∞- groupoids, that was first conjectured by A. Grothendieck, and describe its prominent features, If time permits, we will also outline how a comparison with topological spaces can be made quite explicitely, leading to the formulation of the so-called "Homotopy Hypothesis".