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A note on free regular and exact completions and their infinitary generalizations. (English) Zbl 0872.18004
The main result presents the free regular and exact completions of a weakly lex category \({\mathcal C}\) as full subcategories of the presheaf category \({\mathcal S} et^{{\mathcal C}^{op}}\). This new and very nice description is based on an idea of G. M. Kelly.

MSC:
18E10 Abelian categories, Grothendieck categories
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
18G05 Projectives and injectives (category-theoretic aspects)
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