Internal categories in Mal'cev categories
The main result of this article is that the category of internal categories and functors in a Mal'cev exact category is again a Mal'cev exact category (exactness here is in the sense of \textit{M. Barr}). This result applies not only to categories of groups, rings, Lie algebras etc., but also to some non-varietal categories such as the duals of the categories of abelian groups and of compact Hausdorff spaces. A regular category \({\mathcal C}\) is a Mal'cev category iff every reflexive relation in \({\mathcal C}\) is in fact an equivalence relation. [For other formulations, see \textit{A. Carboni}, \textit{J. Lambek} and \textit{M. C. Pedicchio}, ``Diagram chasing in Mal'cev categories'', J. Pure Appl. Algebra 69, No. 3, 271-284 (1990; Zbl 0722.18005).] After some needed preliminaries on Mal'cev categories, the bulk of the paper is taken up with the proof of the main result.
category of internal categories and functors
scientific article; zbMATH DE number 1384149