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:
“The American people owe it to themselves, and to the cause of free Government, to prove by their establishments for the advancement and diffusion of knowledge, that their political Institutions ... are as favorable to the intellectual and moral improvement of Man as they are conformable to his individual and social rights.”
—James Madison (1751–1836)
“Example is a bright looking-glass, universal and for all shapes to look into.”
—Michel de Montaigne (1533–1592)