Free Universal Algebras
Let be any set, let be an algebraic structure of type generated by . Let the underlying set of this algebraic structure, sometimes called universe, be, and let be a function. We say that, (or informally just ) is a free algebra (of type ) on the set of free generators if, for every algebra of type and function, where is a universe of, there exists a unique homomorphism such that .
Read more about this topic: Free Object
Famous quotes containing the words free and/or universal:
“It is remarkable how many creatures live wild and free though secret in the woods, and still sustain themselves in the neighborhood of towns, suspected by hunters only.”
—Henry David Thoreau (1817–1862)
“The Universal Soul, as it is called, has an interest in the stacking of hay, the foddering of cattle, and the draining of peat-meadows.”
—Henry David Thoreau (1817–1862)