We show that there are infinitely many distinct closed classes of colimits (in the sense of the Galois connection induced by commutation of limits and colimits in Set) which are intermediate between the class of pseudo-filtered colimits and that of all (small) colimits. On the other hand, if the corresponding class of limits contains either pullbacks or equalizers, then the class of colimits is contained in that of pseudo-filtered colimits.
Keywords: Limit, colimit, filtered colimit, group action, simple group, Galois connection
2010 MSC: 18A30, 18B05, 20J99
Theory and Applications of Categories, Vol. 30, 2015, No. 15, pp 527-532.