Lack, Stephen A note on the exact completion of a regular category, and its infinitary generalizations. (English) Zbl 0912.18004 Theory Appl. Categ. 5, 70-80 (1999). A description is given of the exact completion \(\mathcal C_{\text{ex/reg}}\) of a small regular category \(\mathcal C\) as a full subcategory of \(Set^{\mathcal C^{\text{op}}}\). A classical construction of \(\mathcal C_{\text{ex/reg}}\) [see A. Carboni and E. M. Vitale, “Regular and exact completions”, J. Pure Appl. Algebra 125, No. 1-3, 79-116 (1998; Zbl 0891.18002)] uses the category \(\text{Rel}(\mathcal C)\) of relations in \(\mathcal C\). Reviewer: J.Rosický (Brno) Cited in 11 Documents MSC: 18A35 Categories admitting limits (complete categories), functors preserving limits, completions 18E10 Abelian categories, Grothendieck categories 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) Keywords:regular category; exact category; exact completion; category of sheaves Citations:Zbl 0891.18002 PDFBibTeX XMLCite \textit{S. Lack}, Theory Appl. Categ. 5, 70--80 (1999; Zbl 0912.18004) Full Text: EuDML EMIS