ABSTRACT
This chapter deals with some additional matters from homological algebra. It considers some applications of pullbacks and pushouts to short exact sequences. This sum is called the Baer sum. In the theory of homological algebra and its applications there is a very important result which is often known as the “snake lemma”. This lemma consists of two parts: the construction of an exact sequence, which is often called “kernel-cokernel sequence”, for any commutative diagram of a special type; and the construction of long exact sequences of homology groups for any given short exact sequence of complexes. Following R. Baer the addition of extensions of modules, which makes the set of equivalence classes of all extensions an Abelian group. The chapter describes the proof of the first part of the statement which is well known as the snake lemma.
