Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Definition 2.1.0.3. A nonunital monoid is a set $M$ equipped with a map

\[ m: M \times M \rightarrow M \quad \quad (x,y) \mapsto xy \]

which satisfies the associative law $x(yz) = (xy)z$ for $x,y,z \in M$.