# short exact sequence

Let $A,B,C$ be objects in an abelian category^{}. A
is an exact sequence^{} of the form

$$0\to A\to B\to C\to 0.$$ |

Note that in this case,
the homomorphism^{} $A\to B$
must be a monomorphism^{},
and the homomorphism $B\to C$
must be an epimorphism^{}.

Title | short exact sequence^{} |
---|---|

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 |