# Definition:Object (Category Theory)

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## 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.

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

## Also see

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**object** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**object** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**object**