Introduction
“The slogan is ‘Adjoint functors arise everywhere’.” (Saunders Mac Lane, Categories for the working mathematician)
The long list of examples in this article is only a partial indication of how often an interesting mathematical construction is an adjoint functor. As a result, general theorems about left/right adjoint functors, such as the equivalence of their various definitions or the fact that they respectively preserve colimits/limits (which are also found in every area of mathematics), can encode the details of many useful and otherwise non-trivial results.
Read more about this topic: Adjoint Functors
Famous quotes containing the word introduction:
“My objection to Liberalism is this—that it is the introduction into the practical business of life of the highest kind—namely, politics—of philosophical ideas instead of political principles.”
—Benjamin Disraeli (1804–1881)
“For the introduction of a new kind of music must be shunned as imperiling the whole state; since styles of music are never disturbed without affecting the most important political institutions.”
—Plato (c. 427–347 B.C.)
“Do you suppose I could buy back my introduction to you?”
—S.J. Perelman, U.S. screenwriter, Arthur Sheekman, Will Johnstone, and Norman Z. McLeod. Groucho Marx, Monkey Business, a wisecrack made to his fellow stowaway Chico Marx (1931)