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:
“Others apart sat on a Hill retir’d,
In thoughts more elevate, and reason’d high
Of Providence, Foreknowledge, Will, and Fate,
Fixt Fate, free will, foreknowledge absolute,
And found no end, in wandring mazes lost.
Of good and evil much they argu’d then,
Of happiness and final misery,
Passion and Apathie, and glory and shame,
Vain wisdom all, and false Philosophie:”
—John Milton (1608–1674)
“I believe there’s no proverb but what is true; they are all so many sentences and maxims drawn from experience, the universal mother of sciences.”
—Miguel De Cervantes (1547–1616)