Two-dimensional regularity and exactness (Q2436719)

The paper deals with 2-dimensional generalizations of the notions of regular and exact category. It is based on the theory of lex colimits [\textit{R. Garner} and \textit{S. Lack}, J. Pure Appl. Algebra 216, No. 6, 1372--1396 (2012; Zbl 1256.18002)] and unifies existing approaches. In detail, the authors consider three particular notions of 2-dimensional regularity and exactness depending on three important factorization systems on Cat.