# Definition:Object (Category Theory)

## Definition

Let $\mathbf C$ be a metacategory.

An object of $\mathbf C$ is an object which is considered to be atomic from a category theoretic perspective.

It is a conceptual device introduced mainly to make the discussion of morphisms more convenient.

Objects in a general metacategory are usually denoted with capital letters like $A,B,C,X,Y,Z$.

The collection of objects of $\mathbf C$ is denoted $\mathbf C_0$.

That objects don't play an important role in category theory is apparent from the fact that the notion of a metacategory can be described while avoiding to mention objects altogether.

Nonetheless the notion of object is one of the two basic concepts of metacategories and as such of category theory.