Stable homotopy theory
A section of a morphism in some category is a right-inverse: a morphism such that
equals the identity morphism on .
In the case that has a section , may also be called a retraction or cosection of , may be called a retract of , and the entire situation is said to split the idempotent
A split epimorphism is a morphism that has a section; a split monomorphism is a morphism that is a section. A split coequalizer is a particular kind of split epimorphism.
Sections of bundles and sheaves
If one thinks of as a bundle then its sections are sometimes called global sections. This leads to a notion of global sections of sheaves and further of objects in a general topos. See
for more on this.
Revised on August 22, 2013 05:12:40
by Urs Schreiber