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:
“This leads us to note down in our psychological chart of the mass-man of today two fundamental traits: the free expansion of his vital desires, and, therefore, of his personality; and his radical ingratitude towards all that has made possible the ease of his existence. These traits together make up the well-known psychology of the spoilt child.”
—José Ortega Y Gasset (1883–1955)
“The exuberant fertility of the universal will.”
—Friedrich Nietzsche (1844–1900)