Three
basic theorems, confusingly more about the behaviour of
homomorphisms than that of
isomorphisms (they show what certain objects generated using a homomorphism are
isomorphic to). These are considerably more
universal than would appear;
natural generalisations hold outside
group theory, e.g. in
ring theory,
linear algebra, and more exotic areas. In the
language of
category theory, they hold for
Abelian categories, of which these are all
examples.
Note the exceedingly original terminology: