\begin{definition}[Definition:Language of Category Theory]
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 $\operatorname{Cdm}$, 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.
\end{definition}