Describing the Bool-And monoid in terms of categories
Monoids are one-object categories. The elements are morphisms, monoid multiplication is composition and the monoid identity is the identity morphism.

In the case of Booleans-with-AND the monoid is $M = (\{\top, \bot\}, \land, \top)$. The category therefore has a single object (we could call it $M$) with two morphisms $\top : M \to M$ and $\bot : M \to M$. Composition is given by $\land$ and the identity morphism is $\top$.



To give a little more context, there is a way to view a monoid in such a way that the objects are the elements of the monoid: as a discrete (no non-identity morphisms) monoidal category. Category Theory for Programmers covers the topic of monoidal categories in Chapter 22, "Monads Categorically".