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27 lines
1.0 KiB
27 lines
1.0 KiB
# byconj.gd RAQ Quandles by conjugation
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# The following outline of defining c
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DeclareCategory("IsConjugatorObject",
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IsMultiplicativeElement and IsLeftQuotientElement and
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IsLSelfDistElement and IsIdempotent);
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DeclareCategoryCollections("IsConjugatorObject");
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DeclareAttribute("ConjugatorFamily", IsFamily);
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DeclareAttribute("ConjugatorType", IsFamily);
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DeclareSynonym("IsDefaultConjugatorObject",
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IsConjugatorObject and IsPositionalObjectOneSlotRep);
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# As far as I can tell, we are not losing any generality here;
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# to define the conjugator, we need the quotient on one side, to define
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# left quotients of conjugators we need the quotient on the other side, and
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# to prove it works we need associativity, which makes the underlying elements
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# of conjugator objects automatically group elements.
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DeclareAttribute("ConjugatorObj", IsMultiplicativeElementWithInverse);
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DeclareAttribute("UnderlyingMultiplicativeElement", IsConjugatorObject);
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# The meat of the matter:
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DeclareAttribute("ConjugationQuandle", IsGroup);
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