In various branches of mathematics, a useful construction is often viewed as the “most efficient solution” to a certain problem. The definition of a universal property uses the language of category theory to make this notion precise and to study it abstractly.
This article gives a general treatment of universal properties. To understand the concept, it is useful to study several examples first, of which there are many: all free objects, direct product and direct sum, free group, free lattice, Grothendieck group, product topology, Stone–Čech compactification, tensor product, inverse limit and direct limit, kernel and cokernel, pullback, pushout and equalizer.
Read more about Universal Property: Motivation, Formal Definition, Duality, Examples, History
Famous quotes containing the words universal and/or property:
“The universal regard for money is the one hopeful fact in our civilisation. Money is the most important thing in the world. It represents health, strength, honour, generosity and beauty.... Not the least of its virtues is that it destroys base people as certainly as it fortifies and dignifies noble people.”
—George Bernard Shaw (1856–1950)
“Only the old are innocent. That is what the Victorians understood, and the Christians. Original sin is a property of the young. The old grow beyond corruption very quickly.”
—Malcolm Bradbury (b. 1932)