In a commutative diagram of short exact sequences, if the maps on both outer terms are isomorphisms, then the map on the middle terms is an isomorphism.
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The Short Five Lemma is a tool in algebraic topology, specifically in the context of homological algebra and the theory of derived functors. It deals with the properties of cohomology in the setting of a commutative diagram of chain complexes and can be used to derive relationships between cohomology groups of various objects.