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Induced homomorphism
・ Induced homomorphism (algebraic topology)
・ Induced homomorphism (fundamental group)
・ Induced homomorphism (quotient group)
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Induced homomorphism : ウィキペディア英語版
Induced homomorphism
In mathematics, an induced homomorphism is a structure-preserving map between a pair of objects that is derived in a canonical way from another map between another pair of objects.
==In topology==
A particularly important case arises in algebraic topology, where any continuous function between two pointed topological spaces induces a group homomorphism between the fundamental groups of the two spaces. (See section III.5.4, p. 201, in H. Schubert.)


Likewise, the same continuous map induces a group homomorphism between the respective homotopy groups, the respective homology groups (IV.1.3, pp. 240–241) 〔 and a homomorphism going in the opposite direction between the corresponding cohomology groups (IV.4.2-3, pp. 298–299).〔

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