Assertion: isomorphism's inverse | /r/HasProperty | homomorphism
Facets:
Source sentences:
text: Since log {\displaystyle \log } is a homomorphism that has an inverse that is also a homomorphism, log {\displaystyle \log } is an isomorphism of groups.
text: A suggestion: replace "an isomorphism is a morphism that admits a two-sided inverse" with "an isomorphism is a homomorphism of which the inverse is also a homomorphism".
text: It is a bit better to say that an isomorphism of partially ordered sets is a homomorphism that has an inverse that is also a homomorphism; this gives you the biconditional as a consequence, rather than as a premise, and it makes it fit into the general scheme better.
text: The definition works in the context of groups, rings, semigroups, fields, etc., but it turns out that in those cases, being a bijective homomorphism suffices to guarantee that the set-theoretic inverse is also a homomorphism.)
text: I must show the inverse is a homomorphism.
text: An isomorphism is a bijective homomorphism whose inverse is also homomorphism.