Section (category theory)
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In the mathematical field of category theory, given a pair of maps 
, 
such that fg = idY (the identity map on Y), we call g a section of f, and f a retraction of g. In other words, a section is a right inverse, and a retraction is a left inverse (and these are dual notions).
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.
A section is a monomorphism, and a retraction is an epimorphism; they are called respectively a split monomorphism and a split epimorphism (the inverse is the splitting).
[edit] Examples
Given a quotient space 
with quotient map 
, a section of π is called a transversal.
