short exact sequence

Let A,B,C be objects in an abelian categoryMathworldPlanetmathPlanetmathPlanetmath. A is an exact sequenceMathworldPlanetmathPlanetmathPlanetmathPlanetmath of the form


Note that in this case, the homomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath AB must be a monomorphismMathworldPlanetmathPlanetmath, and the homomorphism BC must be an epimorphismMathworldPlanetmath.

Title short exact sequenceMathworldPlanetmathPlanetmath
Canonical name ShortExactSequence
Date of creation 2013-03-22 12:09:29
Last modified on 2013-03-22 12:09:29
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 7
Author antizeus (11)
Entry type Definition
Classification msc 16E05
Related topic CategoricalSequence