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Short Five Lemma
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Geliefert zwischen Mi., 26.11.2025 und Do., 27.11.2025
Details
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma. It states that for the following commutative diagram (in any abelian category, or in the category of groups), if the rows are short exact sequences, and if g and h are isomorphisms, then f is an isomorphism as well.The essence of the lemma can be summarized as follows: if you have a homomorphism f from an object B to an object B , and this homomorphism induces an isomorphism from a subobject A of B to a subobject A of B and also an isomorphism from the factor object B/A to B /A '''', then f itself is an isomorphism. Note however that the existence of f has to be assumed from the start; two objects B and B that simply have isomorphic sub- and factor objects need not themselves be isomorphic (for example, in the category of abelian groups, B could be the cyclic group of order four and B the Klein four-group).
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131239830
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131239830
- Format Fachbuch
- Titel Short Five Lemma
- Herausgeber Betascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
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