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Essential localizations and infinitary exact completion. (English) Zbl 1022.18001

Using extensively the universality property of the exact completion of a category with weak small limits, the author gives analogous proofs for two new characterization theorems for localizations of varieties of general algebras and of presheaf categories. These characterizations strengthen existing results in so far as a certain commutation property for products and filtered colimits (AB 6) is assumed only up to a regular epimorphism.

MSC:

18A35 Categories admitting limits (complete categories), functors preserving limits, completions
18E35 Localization of categories, calculus of fractions
18E10 Abelian categories, Grothendieck categories
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18B15 Embedding theorems, universal categories
18C05 Equational categories
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