Category of Categories is Category
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Theorem
Let $\mathbf{Cat}$ be the category of categories.
Then $\mathbf{Cat}$ is a metacategory.
Proof
Let us verify the axioms $(\text C 1)$ up to $(\text C 3)$ for a metacategory.
For any two functors their composition is again a functor by Composite Functor is Functor.
For any small category $\mathbf C$, we have the identity functor $\operatorname {id}_{\mathbf C}$.
By Identity Functor is Left Identity and Identity Functor is Right Identity this is the identity morphism for $\mathbf C$.
Finally by Composition of Functors is Associative, the associative property is satisfied.
Hence $\mathbf{Cat}$ is a metacategory.
$\blacksquare$