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:
“When we our betters see bearing our woes,
We scarcely think our miseries our foes.
Who alone suffers, suffers most i’ the mind,
Leaving free things and happy shows behind.
But then the mind much sufferance doth o’er skip,
When grief hath mates, and bearing fellowship.”
—William Shakespeare (1564–1616)
“We have had many harbingers and forerunners; but of a purely spiritual life, history has afforded no example. I mean we have yet no man who has leaned entirely on his character, and eaten angels’ food; who, trusting to his sentiments, found life made of miracles; who, working for universal aims, found himself fed, he knew not how; clothed, sheltered, and weaponed, he knew not how, and yet it was done by his own hands.”
—Ralph Waldo Emerson (1803–1882)