Generalizing the fact that Scott's continuous lattices form the equational hull of the class of all algebraic lattices, we describe an equational hull of LFP, the category of locally finitely presentable categories, over CAT. Up to a set-theoretical hypothesis this hull is formed by the category of all precontinuous categories, i.e., categories in which limits and filtered colimits distribute. This concept is closely related to the continuous categories of P. T. Johnstone and A. Joyal.
Keywords: locally finitely presentable category, precontinuous category, continuous lattice, pseudomonad
2000 MSC: 18A35, 06B35
Theory and Applications of Categories
, Vol. 11, 2003,
No. 11, pp 252-282.