Object

An object is just a placeholder for the identification of a system, where a system can be composed of many objects, or just a unique object without additional references. In Category Theory, The notion of an object is the most fundamental kind of mathematical data type. It is often distinguished by a label, or a name, assigned by a programmer or a mathematician, to help define the identities of the objects. Objects by themselves can hold a lot of internal information, or it can be just a placeholder designated to help formulate a problem. It is the most generic kind of data representation, so that it is often considred to be the first-class citizen of data representation, especially in the realm of Object-based or Object-Oriented Programming.

Representational Completeness

Object as individual components without inter-relations cannot effectively represent structures of systems. Therefore, there are some special kind of object, made of sequential pairs of objects, can be used as building blocks to represent systems. These kidn of objects are often called Map, basically representing the ordering sequence of two objets. This ordering sequence breaks the symmetrical relations between two objects, and therefore helps define the nature of sequence, or ordering of the system of interest. Map as a relational representation of two objects, can sometimes be considered as a primitive type of functions. They must be composed of two or more objects, including the special case of two identical objects. This kind of data representation is called: composition.