Classifying anima preserves finite products

Proof. This functor factors as \[ \Mon (\An ) \hookrightarrow \sAn \xrightarrow {\abs {-}} \An . \] The geometric realization functor \(\abs {-}\) preserves finite products by Lemma 21.6.12, and the inclusion preserves finite products since monoids are closed under products in \(\sAn \). □