\begin{definition}[Definition:Object (Category Theory)]
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.
{{wtd|That is a big claim which needs a page to back it up; this is demonstrated eg. in 'Categories for the Working Mathematician' by MacLane}}
Nonetheless the notion of '''object''' is one of the two basic concepts of metacategories and as such of category theory.
\end{definition}