clean up of previous commits

examples/ConvertToMapOfFinSets.g

@@ -28,12 +28,12 @@ Display( g );
 #! @EndExample
 
 #! We can also create finite concrete categories with objects 
-#! not starting from 1, to demonstrate that
-#! ConcreteCategoryForCAP( [ [,,,5,6,4], [,,,7,8,9], [,,,,,,8,9,7] ] ) 
-#! and ConcreteCategoryForCAP( [ [2,3,1], [4,5,6], [,,,5,6,4] ] ) yield
-#! equivalent categories, i.e. their underlying quivers are 
-#! the same and they give the same algebroid and category 
-#! of representations.
+#! not starting with $1$, to demonstrate that
+#! <C>ConcreteCategoryForCAP( [ [,,,5,6,4], [,,,7,8,9], [,,,,,,8,9,7] ] )</C>
+#! and <C>ConcreteCategoryForCAP( [ [2,3,1], [4,5,6], [,,,5,6,4] ] )</C> yield
+#! isomorphic categories, in particular, their underlying quivers are
+#! isomorphic (here even equal), inducing isomorphic algebroids and
+#! isomorphic categories of representations.
 
 #! @Example
 ccat := ConcreteCategoryForCAP( [ [2,3,1], [4,5,6], [,,,5,6,4] ] );
@@ -57,6 +57,3 @@ CatReps2 := Hom( A2, GF3 );
 CatReps1 = CatReps2;
 #! true
 #! @EndExample
-
-
-

examples/RelationsOfEndomorphisms.g

@@ -1,31 +1,30 @@
-#! @BeginChunk Endomorphisms
-
-LoadPackage( "CatReps" );
-
-#! 
-#! Two examples to test if RelationsOfEndomorphisms also works
-#! on endomorphisms that aren't bijective.
-#! The first example is a constant endomorphism, so applying
-#! it twice should be the same as once.
-
-#! @Example
-GF3 := HomalgRingOfIntegers(3);
-#! GF(3)
-ccat := ConcreteCategoryForCAP( [ [1,1,1], [4,5,6], [,,,5,6,4] ] );
-#! A finite concrete category
-relEndo := RelationsOfEndomorphisms( GF3, ccat );
-#! [ Z(3)^0*(a*a) + Z(3)*(a), Z(3)^0*(c*c*c) + Z(3)*(2) ]
-#! @EndExample
-
-#! The next example is the permutation by the companion matrix to $a^8-a^3$, so
-#! neither $a^5-a^0$, $a^6-a^1$ nor $a^7-a^2$ are zero:
-
-#! @Example
-GF3 := HomalgRingOfIntegers(3);
-#! GF(3)
-ccat := ConcreteCategoryForCAP( [ [2,3,4,5,6,7,8,4] ] );
-#! A finite concrete category
-relEndo := RelationsOfEndomorphisms( GF3, ccat );
-#! [ Z(3)^0*(a*a*a*a*a*a*a*a) + Z(3)*(a*a*a) ]
-#! @EndExample
-#! @EndChunk
+#! @BeginChunk Endomorphisms
+
+LoadPackage( "CatReps" );
+
+#! The two examples below test <C>RelationsOfEndomorphisms</C>
+#! on endomorphisms that are not bijective.
+
+#! The first generating morphism of the first example is constant, and hence an idempotent.
+
+#! @Example
+GF3 := HomalgRingOfIntegers(3);
+#! GF(3)
+ccat := ConcreteCategoryForCAP( [ [1,1,1], [4,5,6], [,,,5,6,4] ] );
+#! A finite concrete category
+relEndo := RelationsOfEndomorphisms( GF3, ccat );
+#! [ Z(3)^0*(a*a) + Z(3)*(a), Z(3)^0*(c*c*c) + Z(3)*(2) ]
+#! @EndExample
+
+#! The next example is a single permutation defined by the companion matrix of $a^8-a^3$, hence
+#! neither $a^5-a^0$, $a^6-a^1$, nor $a^7-a^2$ are zero:
+
+#! @Example
+GF3 := HomalgRingOfIntegers(3);
+#! GF(3)
+ccat := ConcreteCategoryForCAP( [ [2,3,4,5,6,7,8,4] ] );
+#! A finite concrete category
+relEndo := RelationsOfEndomorphisms( GF3, ccat );
+#! [ Z(3)^0*(a*a*a*a*a*a*a*a) + Z(3)*(a*a*a) ]
+#! @EndExample
+#! @EndChunk