Definition 2.5.4.  Let M be a monoid. We define
(M)
by:
([M, , e]) := M  (M is a set, :M × M → M is an operation on M, e ∈ M such that (M, , e) forms a monoid)
We write “let a ∈ M” for “let a ∈ (M).”
Remarks.

This definition retrieves a representative carrier set from a monoid (which is actually an equivalence class of monoids), and enables typical abuse of notation.