Category Axioms are Self-Dual

Theorem

Morphisms-Only Category Theory

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 $\mathrm{MOCT}$.

Object Category Theory

Let $\mathrm {CT}$ be the collection of seven axioms on Characterization of Metacategory via Equations.

Then:

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

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

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 3.1$