Exact sequence

Short exact sequence

A short exact sequence is an exact sequence with no more than three non-trivial objects, homology i.e. it is of the form

⋯→0→𝐴𝑓↪𝐵𝑔↠𝐶→0→⋯

A morphism of short exact sequences is a triple (𝛼,𝛽,𝛾) of homomorphisms such that the expected commutative diagram commutes.

Properties

1. 𝑓 is guaranteed to be injective and 𝑔 to be surjective (see Properties)
2. Split short exact sequence

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