On Mon, Jun 15, 2015 at 12:07 AM, 'Martin R' via sage-devel <
sage-devel@googlegroups.com> wrote:

> Hi there!
>
> I would like to understand the (intended) purpose of the three classes
> Map, Morphism and PoorManMap.
>
> What I know so far:
>
> * Morphism inherits from Map, and provides a few more methods, in
> particular category, is_endomorphism, is_identity.
>
> * Map itself is used only in very few places, it appears to play a
> somewhat "internal" role.
>
> * Map, Morphism and PoorManMap all assume that the map can be applied to
> elements.  However, PoorManMap does not assume that domain and codomain are
> parents.
>
> My main question is why Map and Morphism are separate classes and whether
> it would make sense to have a more basic class, eg "CategoryMorphism",
> which provides composition of abstract morphisms between CategoryObjects.
>

Seems reasonable, if we actually have some examples to implement of
CategoryObject which are not parents, where we can do nontrivial
compositions of the morphisms.
David

>
> Martin
>
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