Cellular categories (Q2443277)

The authors introduce cellular categories as categories equipped with a class of morphisms containing all isomorphisms and closed under pushout and transfinite composite and prove that these categories are closed under 2-limits, in particular under pseudopullbacks. As notation, \textbf{CELL} denotes the 2-category of cellular categories, cellular functors and natural transformations; and \textbf{COMB} denotes the 2-category of combinatorial categories, combinatorial functors and natural transformations. Among the main results they prove that the category \textbf{CELL} has pseudopullbacks and the category \textbf{COMB} has pseudopullbacks calculated in \textbf{CELL}.