a hopfian object is an object A such that any epimorphism of A onto A is necessarily an automorphism. The dual notion is that of a cohopfian object, which...

group theory, a co-Hopfian group is a group that is not isomorphic to any of its proper subgroups. The notion is dual to that of a Hopfian group, named after...

the field of pure mathematics. Co-Hopfian group Cohomotopy group EHP spectral sequence Hopfian group Hopfian object Quantum group Alexandroff P., Hopf...

automorphism of M. This says simply that M is a Hopfian module. Similarly, an Artinian module M is coHopfian: any injective endomorphism f is also a surjective...