# Definition:Language of Category Theory

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## Definition

The language of **(morphisms-only) category theory** is a specific instance of the language of predicate logic.

As such, it is considered to have:

- unary function symbols $\operatorname{dom}$ and $\operatorname{cod}$, called the
**domain**and**codomain**symbols - A ternary relation symbol $R_\circ$, called the
**composition relation**symbol

All further descriptions required to determine a formal language are inherited from the definition of the language of predicate logic.

## Remark

The definition as given here is for *morphisms-only* category theory, since having to distinguish between objects and morphisms would give rise to a very tedious and technical mess.