Maximal semilattice quotient

In the context of algebra and order theory, a **semilattice** is an algebraic structure consisting of a set equipped with an associative and commutative binary operation that has an identity element. Semilattices can be classified into two main types: **join-semilattices**, where the operation is the least upper bound (join), and **meet-semilattices**, where the operation is the greatest lower bound (meet).