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:
“Exporting Church employees to Latin America masks a universal and unconscious fear of a new Church. North and South American authorities, differently motivated but equally fearful, become accomplices in maintaining a clerical and irrelevant Church. Sacralizing employees and property, this Church becomes progressively more blind to the possibilities of sacralizing person and community.”
—Ivan Illich (b. 1926)
“I have no concern with any economic criticisms of the communist system; I cannot enquire into whether the abolition of private property is expedient or advantageous. But I am able to recognize that the psychological premises on which the system is based are an untenable illusion. In abolishing private property we deprive the human love of aggression of one of its instruments ... but we have in no way altered the differences in power and influence which are misused by aggressiveness.”
—Sigmund Freud (1856–1939)