Constructing span categories from categories without pullbacks

Constructing TQFTs from Categories of Sheaves

In this talk, I’ll try to synthesise some of the ideas from the earlier talks in order to describe an example of a fully extended 2d TQFT. This TQFT will be built from geometric data following the “bottom-up” approach of the cobordism hypothesis. That is, we’ll choose a category of geometric objects (quashicoherent sheaves on a stack) to assign to the point, and explore some of the consequences...

Semi-pullbacks and Bisimulations in Categories of Stochastic Relations

Constructing Differential Categories and Deconstructing Categories of Games

We present an abstract construction for building differential categories useful to model resource sensitive calculi, and we apply it to categories of games. In one instance, we recover a category previously used to give a fully abstract model of a nondeterministic imperative language. The construction exposes the differential structure already present in this model. A second instance correspond...

Semi-pullbacks and bisimulation in categories of Markov processes

Received We show that the category whose objects are famidclies of Markov processes on Polish spaces, with a given transition kernel, and whose morphisms are transition probability preserving, surjective continuous maps has semi-pullbacks, i.e. for any pair of morphisms fi : Si ! S (i = 1; 2), there exists an object V and morphisms i : V ! Si (i = 1; 2) such that f1 1 = f2 2. This property hold...

QUILLEN THEOREMS Bn FOR HOMOTOPY PULLBACKS OF (∞, k)-CATEGORIES

We extend the Quillen Theorem Bn for homotopy fibers of Dwyer et al. to similar results for homotopy pullbacks and note that these results imply similar results for zigzags in the categories of relative categories and k-relative categories, not only with respect to their Reedy structures but also their Rezk structure, which turns them into models for the theories of (∞, 1)and (∞, k)-categories ...