Categories

Abstract

We have often referred to certain types of Fig. 29.1. Categories are the smiley of contemporary mathematics. structures—sets, monoids, groups, rings, digraphs, or modules—where there was a shared structural characteristic: All of these structures have objects (such as sets, monoids, groups, etc.) and a type of “function” (set functions, monoid morphisms, digraph morphisms, etc.). And all of these functions can be composed if domains and codomains can be ‘concatenated.’ The common denominator of these structures is the concept of a category.