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 experience of the gangster as an experience of art is universal to Americans. There is almost nothing we understand better or react to more readily or with quicker intelligence.... In ways that we do not easily or willingly define, the gangster speaks for us, expressing that part of the American psyche which rejects the qualities and the demands of modern life, which rejects “Americanism” itself.”
—Robert Warshow (1917–1955)
“Communism is inequality, but not as property is. Property is exploitation of the weak by the strong. Communism is exploitation of the strong by the weak.”
—Pierre-Joseph Proudhon (1809–1865)