Dictionary
Thesaurus
Reference
Translate
Web
Section (category theory)
1 reference results for: Section (category theory)
Wikipedia
In category theory, a branch of mathematics, a section is a right inverse of a morphism. Dually, a retraction is a left inverse. In other words, if fcolon Xto Y and gcolon Yto X are morphisms whose composition fgcolon Yto Y is the identity morphism on Y, then g is a section of f, and f is a retraction of g.

The categorical concept of a section is important in homological algebra, and is also closely related to the notion of a section of a fiber bundle in topology: in the latter case, a section of a fiber bundle is a section of the bundle projection map of the fiber bundle.

Every section is a monomorphism, and every retraction is an epimorphism; they are called respectively a split monomorphism and a split epimorphism (the inverse is the splitting).

Examples

Given a quotient space bar X with quotient map picolon X to bar X, a section of pi is called a transversal.

See also

Wikipedia, the free encyclopedia © 2001-2006 Wikipedia contributors (Disclaimer)
This article is licensed under the GNU Free Documentation License.
Last updated on Thursday July 10, 2008 at 16:55:14 PDT (GMT -0700)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

CITE THIS SOURCE|PRINT
Share This:Share This: digg.comShare This: ma.gnolia.comShare This: www.stumbleupon.comShare This: del.icio.usShare This: FacebookShare This: favorites.live.comShare This: www.technorati.comShare This: furl.netShare This: myweb2.search.yahoo.comShare This: www.google.com