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 Topics FrontPage Aldor FriCAS language SandBox SandBox Aldor Category Theory SandBox Aldor Category Theory 7 <-- You are here. aldor#pile #include "axiom" +++ +++ Quotients +++ define Quotient(Obj:Category):Category == with Quotient: (A:Obj,B:Obj) -> (A->B) -> (Quo:Obj,A->Quo,(X:Obj)->(A->X)->(Quo->X)) /:(A:Obj,B:Obj) -> ((A->B)->Obj) default (A:Obj)/(B:Obj):((A->B)->Obj) == F(f:A->B):Obj == (Q:Obj,insert:A->Q,quo:(X:Obj)->(A->X)->(Q->X)) == Quotient(A,B)(f) Q add F +++ +++ Subobjects (the dual of Quotients) +++ define Subobject(Obj:Category):Category == with Subobject: (A:Obj,B:Obj) -> (B->A) -> (Sub:Obj,Sub->A,(X:Obj)->(X->A)->(X->Sub)) \:(A:Obj,B:Obj) -> ((B->A)->Obj) default (A:Obj)\(B:Obj):(B->A)->Obj == F(f:(B->A)): Obj == (S:Obj,include:S->A,sub:(X:Obj)->(X->A)->(X->S)) == Subobject(A,B)(f) S add F aldor Compiling FriCAS source code from file /var/zope2/var/LatexWiki/subobjects.as using AXIOM-XL compiler and options -O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I$AXIOM/algebra Use the system command )set compiler args to change these options. Compiling Lisp source code from file ./subobjects.lsp Issuing )library command for subobjects Reading /var/zope2/var/LatexWiki/subobjects.asy Quotient is now explicitly exposed in frame initial Quotient will be automatically loaded when needed from /var/zope2/var/LatexWiki/subobjects Subobject is now explicitly exposed in frame initial Subobject will be automatically loaded when needed from /var/zope2/var/LatexWiki/subobjects >> System error: The bounding indices 163 and 162 are bad for a sequence of length 162. See also: The ANSI Standard, Glossary entry for "bounding index designator" The ANSI Standard, writeup for Issue SUBSEQ-OUT-OF-BOUNDS:IS-AN-ERROR

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