Having established Matrix Categories,
we can now define the metalogic of logics
to be the monad completion ****of $\mathbb{M}\mathrm{at}\mathbb{C}\mathrm{at}$.
<aside> ⚠️ All definitions will be given in both images and diagrams. For now, use the correspondence below, and Matrix Categories.
</aside>
Note. To present coherence equations, we use the symbol
$$ ⁍ $$
to denote that the two transformations from $x$ to $y$,
inferrable from context, are equal.
For example, in meta inference,
the coherence with the center associators is drawn and denoted
