# Category Axioms are Self-Dual/Morphisms-Only Category Theory

## Theorem

Let $\mathrm{MOCT}$ be the collection of axioms for morphisms-only category theory.

Then:

$\mathrm{MOCT} = \mathrm{MOCT}^*$

where $\mathrm{MOCT}^*$ consists of the dual statements of those in $\mathrm{MOCT}$.