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:
“We have to hate our immediate predecessors to get free of their authority.”
—D.H. (David Herbert)
“Vanity, or to call it by a gentler name, the desire of admiration and applause, is, perhaps, the most universal principle of human actions.... Where that desire is wanting, we are apt to be indifferent, listless, indolent, and inert.... I will own to you, under the secrecy of confession, that my vanity has very often made me take great pains to make many a woman in love with me, if I could, for whose person I would not have given a pinch of snuff.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)