Free regular and exact completions of categories with various ranks of weak limits are presented as subcategories of presheaf categories. Their universal properties can then be derived with standard techniques as used in duality theory.
Keywords: regular category, exact category, regular completion, exact completion, flat functor, accessible category.
AMS Classification (1991): 18A35, 18E10, 18G05.
Theory and Applications of Categories, Vol. 2, 1996, No. 10, pp113-132.
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