I will present a theorem saying that homotopical functors out of a cofibration category are essentially determined by its subcategory of cofibrations. As an application I will discuss a functorial construction of groupoid $C^*$-algebras which is related to the Baum-Connes Conjecture. This is joint work with Markus Land and Thomas Nikolaus.

Generalized K\"ahler manifold is the analogue of K\"ahler manifold in the framework of generalized geometry \`a la Hitchin. Many non-K\"ahler complex manifolds admit generalized K\"ahler structures. In this context, the analogue of a holomorphic bundle is a $\mathbb{J}$-holomorphic bundle, where $\mathbb{J}$ is one of the generalized complex structures. We will discuss some examples of these objects, a possible candidate for stability and the Kobayashi-Hitchin correspondence in this context.

Speaker's homepage: https://legacy.wlu.ca/homepage.php?grp_id=12368&f_id=43

This talk will introduce two new models of infinity categories (simplicially-enriched categories and relative categories), and relate them to quasicategories.