×

A note on the exact completion of a regular category, and its infinitary generalizations. (English) Zbl 0912.18004

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)

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)

Citations:

Zbl 0891.18002
PDFBibTeX XMLCite
Full Text: EuDML EMIS