Fibration categories and opetopic sets

Christian Sattler, University of Leeds. Part of the algebra seminar series.

Homotopy theories, i.e. (omega,1)-categories, are traditionally presented using model categories, but can also be presented using the weaker notion of fibration category. Fibration categories are easier to construct than model categories, and although they do not support the full range of constructions known from model categories, often it is easier to see a higher-dimensional entity as an object of a fibration category. For example, simplicial sets form a model category, but semisimplicial sets only form a fibration category.

In this talk, we will look at certain presentations of higher categories in (marked) presheaves over a category C. A standard example is Verity\'s model structure on weak complicial sets, where C = Delta. When C is direct, one typically only obtains a fibration category. This is the case for opetopic sets, for which we will give a detailed introduction. If time permits, we will examine a route for relating these two models by constructing an intermediate model in weak semicomplicial sets.

 After each talk at 4:15pm there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber. 

Christian Sattler, University of Leeds