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 $\operatorname{Cdm}$, 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.
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.