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 hero is a mind of such balance that no disturbances can shake his will, but pleasantly, and, as it were, merrily, he advances to his own music, alike in frightful alarms and in the tipsy mirth of universal dissoluteness.”
—Ralph Waldo Emerson (1803–1882)
“As a man is said to have a right to his property, he may equally be said to have a property in his rights.”
—James Madison (1751–1836)