Natural homomorphisms

On page 3 of Elrifai and Morton's "Algorithms for positive braids",
they state "The abelianisation map defines a natural homomorphism wt:
B_n -> Z". But I can't understand how this can be a natural
homomorphism when such a mapping is from some group G to G/N (N being
a normal subgroup of G). Does anybody know what's going on here?

Thanks,

James McLaughlin.
.

Relevant Pages

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