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:
“It is impossible that anything so natural, so necessary, and so universal as death should ever have been designed by Providence as an evil to mankind.”
—Jonathan Swift (1667–1745)
“Children are potentially free and their life directly embodies nothing save potential freedom. Consequently they are not things and cannot be the property either of their parents or others.”
—Georg Wilhelm Friedrich Hegel (1770–1831)