# Section of a mapping

From Encyclopedia of Mathematics

A mapping for which . In a wider sense, a section of any morphism in an arbitrary category is a right-inverse morphism.

#### Comments

If is a subspace of , a section over of is a mapping such that for all . For a vector bundle , where the mapping is part of the structure defined, one speaks of a section of the vector bundle rather than of a section of . This applies, e.g., also to sheaves and fibrations. A standard notation for the set of sections in such a case is , or for the set of sections of over .

**How to Cite This Entry:**

Section of a mapping.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Section_of_a_mapping&oldid=18495

This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article