Colimits of accessible categories (Q2841498)

The \(2\)-category of accessible categories and accessible functors is known to have all appropriate limits, but there is not much known about colimits. In this paper the authors consider directed colimits. They show that directed colimits of accessible categories and accessible full embeddings are accessible, and they obtain a similar result for arbitrary accessible embeddings on the assumption that there are arbitrarily large strongly compact cardinals. They do not know whether the assumption about cardinals is necessary.