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:
“All progress is based upon a universal innate desire on the part of every organism to live beyond its income.”
—Samuel Butler (1835–1902)
“It is as if being was to be observed,
As if, among the possible purposes
Of what one sees, the purpose that comes first,
The surface, is the purpose to be seen,
The property of the moon, what it evokes.”
—Wallace Stevens (1879–1955)