 Second and alternatively, there is a categorical notion of structure based on the primitive concept of morphisms between mathematical objects. Typically, a category consists of two types of entities, namely objects and morphisms between them, i.e., mappings represented by arrows that preserve some of the internal structural composition of the objects. An axiom system that defines the general concept of a category, along such lines, was first introduced by Eilenberg and Mac Lane (1945). It describes a suitable composition operation on arrows, its associativity, as well as the existence of an identity morphism for each object (cf. Awodey 2010 for a textbook presentation of category theory).