Paige North:Weak factorization systems and display map categories

In this talk, I will describe the relationship between weak factorization systems and display map categories modeling Pi, Sigma, and/or Id types. When an ambient category C is Cauchy complete, the problem of finding the structure of a display map category modeling Sigma and Id types within C reduces to a problem of characterizing weak factorization systems on C. I will describe the categories of these objects, and using this framework I will describe the relationship between display map categories modeling Id types and those modeling Pi types.