Categories

Abstract

A category has objects and morphisms. The latter can be composed. We have no immediate access to internal structure of objects. Thus all properties must be expressed in terms of morphisms. For example we met briefly the Initial Model which was characterised by the fact that there was a unique morphism from it to any other model. In Set, the empty set has a similar property whereas a singleton set has the property that there is a unique function from any other set to it. The next article will investigate such constructions which can be defined simply in terms of the existence and properties of morphisms.