Section (category Theory)
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 and are morphisms whose composition is the identity morphism on, then is a section of, and is a retraction of .
Every section is a monomorphism, and every retraction is an epimorphism; in algebra the sections are also called split monomorphisms and the retractions split epimorphisms.
In an abelian category, if f:X→Y is a split epimorphism with section g:Y→X, then X is isomorphic to the direct sum of Y and the kernel of f.
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