[Haskell-cafe] Endo a, endomorphisms

[Adrian]

‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐

On Sunday, December 5th, 2021 at 8:13 AM, Tom Ellis <tom-lists-haskell-cafe-2017 at jaguarpaw.co.uk> wrote:

> On Sun, Dec 05, 2021 at 02:02:09PM +0000, Adrian via Haskell-Cafe wrote:
>
> > In the Data.Monoid library there is a monoid type instance for Endo
> >
> > a that is described in the following manner:
> >
> > > The monoid of endomorphisms under composition.
> >
> > I understand how it is a monoid of endofunctions, but am unclear on
> >
> > how it is a monoid of endomorphisms.
>
> I'm not sure what you mean. The morphisms in this case are exactly
>
> functions. "Endomorphism" and "endofunction" have the same meaning in
>
> this context.
>
> Tom
>

According to Algebra [Hungerford 74], an endomorphism is an endofunction that is a homomorphism.
A set of endomorphisms is quite distinct from a set of endofunctions in this regard.