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 God whom science recognizes must be a God of universal laws exclusively, a God who does a wholesale, not a retail business.”
—William James (1842–1910)
“For wisdom is the property of the dead,
A something incompatible with life; and power,
Like everything that has the stain of blood,
A property of the living; but no stain
Can come upon the visage of the moon
When it has looked in glory from a cloud.”
—William Butler Yeats (1865–1939)