Officially support "Target" instead of "Range"

[zickgraf]

If we want to make Target the new default, we should also discuss and change some other things like ...WithGivenRange and RangeCategoryOfHomomorphismStructure.

Originally posted by @zickgraf in https://github.com/homalg-project/CAP_project/issues/1409#issuecomment-1662411537

@mohamed-barakat @kamalsaleh While rebasing some branches in CategoricalTowers I noticed that you seem to use "Target" instead of "Range" by default now. It would be nice if you could also tackle the points mentioned above to make things consistent. For example, currently a simple search+replace for "Range -> Target" is not possible due to the above points.

[mohamed-barakat]

I am for globally replacing Range with Target. The use of Range is a homalg legacy:

• back then Target was declared as an operation in another package
• Range is the default name for codomains of maps in GAP.

The category theory literature I am aware of uses eitherdomain/codomain or source/target.

Sebastian's paper, where he introduced the Hom-structure uses the notion $B$-homomorphism structure. RangeCategory... is not mentioned in that article. I don't know if WithGivenRange was ever mentioned in one of Sebastian's publications.

[zickgraf]

I am for globally replacing Range with Target.

+ 1

@sebastianpos Would you be fine with this?

The use of Range is a homalg legacy:

* back then `Target` was declared as an operation in another package

* `Range` is the default name for codomains of maps in GAP.

The category theory literature I am aware of uses eitherdomain/codomain or source/target.

I think I have recently seen the use of "range" in some older publication, but I cannot find it anymore right now. In any case, "target" seems to be much more common.

Sebastian's paper, where he introduced the Hom-structure uses the notion B-homomorphism structure. RangeCategory... is not mentioned in that article. I don't know if WithGivenRange was ever mentioned in one of Sebastian's publications.

The papers do mention "range", though.

[sebastianpos]

Yes, I'm fine with this.