Definition:Object (Category Theory)

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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.

Also see