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Long Exact Sequence

4 resources tagged “Long Exact Sequence” across the knowledge library.

4 items

Guide6 Aug 2026Computing Ext GroupsTechniques for computing Ext: choice of variable, use of the long exact sequences, standard computations over the integers, and Ext for cyclic and finitely generated modules.4 min readRead More Guide6 Aug 2026The Long Exact Homology SequenceThe long exact sequence associated to a short exact sequence of complexes, construction of the connecting homomorphism, naturality, and the standard applications.4 min readRead More Guide6 Aug 2026The Long Exact Sequences of Derived FunctorsDerivation of the long exact sequences of derived functors via the horseshoe lemma, their naturality, dimension shifting and the standard computational patterns.3 min readRead More Guide6 Aug 2026The Two Long Exact Sequences of ExtThe long exact sequences of Ext in the first and second variables, their connecting homomorphisms, naturality, and the direction reversal caused by contravariance.3 min readRead More