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:
“If only nature is real and if, in nature, only desire and destruction are legitimate, then, in that all humanity does not suffice to assuage the thirst for blood, the path of destruction must lead to universal annihilation.”
—Albert Camus (1913–1960)
“The property of rain is to wet and fire to burn.”
—William Shakespeare (1564–1616)