The denormalized \(3{\times}3\) lemma
The standard \(3 \times 3\) lemma for groups says that the cokernel of a monomorphism of short exact sequences is short exact, and that the kernel of an epimorphism of short exact sequences is short exact. This paper proves a corresponding statement for a suitably defined notion of short exact sequence in a regular Malcev category. In this context, short exact sequences are replaced by coequalizer diagrams arising from kernel pairs, and the terms ``regular'' and ``Malcev'' refer to the presence of certain exactness conditions on the ambient category.
scientific article; zbMATH DE number 1878454