connecting homomorphism
A crucial concept in homological algebra and algebraic topology, often constructed using the snake lemma to ensure the exactness of sequences.
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Definition
C2Homological Algebra
(technical, academic)A map created using the snake lemma that links the kernels and cokernels in a short exact sequence, forming part of a long exact sequence.
Example
- The connecting homomorphism is essential for constructing the long exact sequence in homology.
- Using the snake lemma, we can derive the connecting homomorphism for our sequence.
C2Algebraic Topology
(technical, academic)A map in exact sequences of chain complexes that helps form long exact sequences of homology groups.
Example
- In algebraic topology, the connecting homomorphism plays a key role in the Mayer-Vietoris sequence.
- The connecting homomorphism ensures the exactness of homology sequences in complex structures.
Similar
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