Definition:Language of Category Theory

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

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 predicate calculus.

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.

Also see

 * Axioms for Morphisms-Only Category Theory
 * Morphisms-Only Metacategory