We give a unified proof of Gabriel-Ulmer duality for locally finitely presentable categories, Adamek-Lawvere-Rosicky duality for varieties and Morita duality for presheaf categories. As an application, we compare presheaf categories and varieties.
Keywords: limit doctrines, locally D-presentable categories, duality.
2000 MSC: 18C10, 18C35, 18A25, 18A30, 18A35.
Theory and Applications of Categories, Vol. 10, 2002, No. 20, pp 486-497.
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