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:
“We early arrive at the great discovery that there is one mind common to all individual men: that what is individual is less than what is universal ... that error, vice and disease have their seat in the superficial or individual nature.”
—Ralph Waldo Emerson (1803–1882)
“Thieves respect property. They merely wish the property to become their property that they may more perfectly respect it.”
—Gilbert Keith Chesterton (1874–1936)