Free "complete semilattices" The construction of free objects depends on the chosen class of morphisms. Functions that preserve all joins (i.e. lower adjoints of Galois connections) are called free complete join-semilattices.
Free "complete semilattices" The construction of free objects depends on the chosen class of morphisms. Functions that preserve all joins (i.e. lower adjoints of Galois connections) are called free complete join-semilattices