positive real numbers. Then, the function defined by the logarithm function is a homomorphism.

Category of groups

If ''h'' : ''G'' -> ''H'' and ''k'' : ''H'' -> ''K'' are group homomorphisms, then so is ''k'' ? ''h'' : ''G'' -> ''K''. This shows that the class of all groups, together with group homomorphisms as morphisms, forms a category (specifically the category of groups).

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