Some prospects for 2-dimensional algebraic exactness properties

The category of categories forms a 2-category. What if we restrict to categories satisfying suitable exactness properties (such as, factorisation of morphisms into a cokernel followed by a kernel) -- does the resulting 2-category of these categories and appropriate functors have a 2-categorical version of those exactness properties? For instance, can we hope that there is a suitable 2-abelian category of abelian categories? These questions seem quite natural, but nevertheless, they are relatively new. In this talk we discuss some of on-going work that addresses them.

The talk will be self-contained and will not assume technical knowledge of either categories or 2-categories.