diff --git a/gap/structure.gd b/gap/structure.gd
index e205e4a..54a4919 100644
--- a/gap/structure.gd
+++ b/gap/structure.gd
@@ -101,3 +101,11 @@ InstallImmediateMethod(GeneratorsOfMagma,
   2,
   q -> GeneratorsOfRightQuasigroup(q)
 );
+
+## Conversions into quasigroup/rack/quandle
+DeclareAttribute("AsLeftQuasigroup", IsCollection);
+DeclareAttribute("AsLeftRack", IsCollection);
+DeclareAttribute("AsLeftQuandle", IsCollection);
+DeclareAttribute("AsRightQuasigroup", IsCollection);
+DeclareAttribute("AsRightRack", IsCollection);
+DeclareAttribute("AsRightQuandle", IsCollection);
diff --git a/gap/structure.gi b/gap/structure.gi
index 05ddab9..758e621 100644
--- a/gap/structure.gi
+++ b/gap/structure.gi
@@ -621,3 +621,49 @@ InstallOtherMethod(DirectProductOp, "for a list and non-quasigroup magma",
     # Not seeing any additional structure; did I miss anything?
     return MagmaByGenerators(gens);
 end);
+
+## Coversions among the structure types
+InstallMethod(AsLeftQuasigroup, "for a left quasigroup", 
+              [IsLeftQuasigroup], IdFunc);
+InstallMethod(AsLeftRack, "for a left rack", 
+              [IsLeftRack], IdFunc);
+InstallMethod(AsLeftQuandle, "for a left quandle", 
+              [IsLeftQuandle], IdFunc);
+InstallMethod(AsRightQuasigroup, "for a right quasigroup", 
+              [IsRightQuasigroup], IdFunc);
+InstallMethod(AsRightRack, "for a right rack", 
+              [IsRightRack], IdFunc);
+InstallMethod(AsRightQuandle, "for a left quandle", 
+              [IsLeftQuandle], IdFunc);
+
+AsAStructure@ := function(struc, D)
+  local T,S;
+  D := AsSSortedList(D);
+  # Check if D is closed under *
+  T := MultiplicationTable(D);
+  if ForAny(T, l -> fail in l) then
+    return fail;
+  fi;  
+  # it is, so check if it satisfies the properties of struc
+  S := struc(D);
+  # OK, good, so we are there, just record what we know
+  SetAsSSortedList(S, D);
+  SetMultiplicationTable(S, T);
+  SetIsFinite(S, true);
+  SetSize(S, Length(D));
+  return S;
+end;
+
+InstallMethod(AsLeftQuasigroup, "for an arbitrary collection",
+  [IsCollection], D -> AsAStructure@(LeftQuasigroup, D));
+InstallMethod(AsLeftRack, "for an arbitrary collection",
+  [IsCollection], D -> AsAStructure@(LeftRack, D));
+InstallMethod(AsLeftQuasigroup, "for an arbitrary collection",
+  [IsCollection], D -> AsAStructure@(LeftQuandle, D));
+
+InstallMethod(AsRightQuasigroup, "for an arbitrary collection",
+  [IsCollection], D -> AsAStructure@(RightQuasigroup, D));
+InstallMethod(AsRightRack, "for an arbitrary collection",
+  [IsCollection], D -> AsAStructure@(RightRack, D));
+InstallMethod(AsRightQuasigroup, "for an arbitrary collection",
+  [IsCollection], D -> AsAStructure@(RightQuandle, D));