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:
“Let us build altars to the Blessed Unity which holds nature and souls in perfect solution, and compels every atom to serve an universal end.”
—Ralph Waldo Emerson (1803–1882)
“Man was born rich, or inevitably grows rich by the use of his faculties; by the union of thought with nature. Property is an intellectual proposition.”
—Ralph Waldo Emerson (1803–1882)