Pattern Recognition

This chapter aims to uncover certain patterns in the considerations of Chs. 2 and 3 and provide evidence for the claim from the introduction to Part I that the presented structure theory of modules would be exemplary for algebraic structures. In particular, we address the parallels mentioned in Section 2.1 between the constructions of sub- and quotient structures for vector spaces, rings, and modules, as well as the repeatedly mentioned naturality of the constructions presented in Ch. 3 . The former leads us to basic concepts of universal algebra, the latter to elementary concepts of category theory.