# byconj.gd RAQ Quandles by conjugation

# The following outline of defining c

DeclareCategory("IsConjugatorObject", 
                IsMultiplicativeElement and IsLeftQuotientElement and
                IsLSelfDistElement and IsIdempotent);
DeclareCategoryCollections("IsConjugatorObject");

DeclareAttribute("ConjugatorFamily", IsFamily);
DeclareAttribute("ConjugatorType", IsFamily);

DeclareSynonym("IsDefaultConjugatorObject",
               IsConjugatorObject and IsPositionalObjectOneSlotRep);

# As far as I can tell, we are not losing any generality here;
# to define the conjugator, we need the quotient on one side, to define
# left quotients of conjugators we need the quotient on the other side, and
# to prove it works we need associativity, which makes the underlying elements
# of conjugator objects automatically group elements.
DeclareAttribute("ConjugatorObj", IsMultiplicativeElementWithInverse);

DeclareAttribute("UnderlyingMultiplicativeElement", IsConjugatorObject);

# The meat of the matter:

DeclareAttribute("ConjugationQuandle", IsGroup);