[tel]

Endomorphism has less implied structure. Lots of dumb things are endomorphisms. Homomorphism implies "structure preservation" which can make it more specific.

[catnaroek]

I'm surprised to read this coming from you.

[dllthomas]

It seems "endomorphism" is used both ways (in, presumably, different contexts).

https://ncatlab.org/nlab/show/endomorphism

I think "endomorphism is a homomorphism ..." is more common, but notably is not the usage in Haskell (https://hackage.haskell.org/package/base/docs/Data-Monoid.ht...)

[catnaroek]

Of course, Haskell's `Endo` is a type constructor for `Hask`-endomorphisms, but more interesting categories exist. Tell me with a straight face ring and field endomorphisms aren't interesting.