On 12 November 2016 at 06:23, Martin Baker <ax87...@martinb.com> wrote:
> ...
> In simpler terms: PermutationGroup and GroupPresentation are never going
> to implement the category 'Group' because in PermutationGroup and
> GroupPresentation % represents the whole group whereas in Group %
> represents an element of the group.
>

I think I know what you mean however in FriCAS % always represents a
domain - not an element of a domain. In the category 'Group' %
represents a domain whose operations satisfy group axioms.  Perhaps it
is unexpected that so few domains in FriCAS satisfy Group but the
requirement is that every value of this type must have a
multiplicative inverse, literally an inverse for the operation *.

PermutationGroup(S) on the other hand is a domain and as you say
values of this type actually represent groups themselves. But % still
represents this domain, not an element of this domain.

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