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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.
Reviewer: J.Rosický (Brno)

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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