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:
“A youthful mind is seldom totally free from ambition; to curb that, is the first step to contentment, since to diminish expectation is to increase enjoyment.”
—Frances Burney (1752–1840)
“Not because Socrates has said it, but because it is really in my nature, and perhaps a little more than it should be, I look upon all humans as my fellow-citizens, and would embrace a Pole as I would a Frenchman, subordinating this national tie to the common and universal one.”
—Michel de Montaigne (1533–1592)