Category of short exact sequences of groups

Definition

The category of short exact sequences of groups is defined as follows:

Aspect	Name	Definition/description
objects	short exact sequences of groups	A short exact sequence of groups is a five-term exact sequence of groups that starts and ends with the trivial group.
morphisms	homomorphism of short exact sequences	homomorphism for each position in the sequence such that the diagram commutes.
composition law for morphisms	composition of homomorphisms	Compose the homomorphism for each group separately.