added Julia support and CategoryOfRepresentations.ipynb

PackageInfo.g

@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 PackageName := "CatReps",
 Subtitle := "Representations and cohomology of finite categories",
 Version := Maximum( [
-                   "2020.07.05", ## Mohamed's version
+                   "2020.09.02", ## Mohamed's version
                    ## this line prevents merge conflicts
                    "2020.07.04", ## Tibor's version
                    ## this line prevents merge conflicts

Project.toml

@@ -0,0 +1,6 @@
+[deps]
+HomalgProject = "50bd374c-87b5-11e9-015a-2febe71398bd"
+IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
+
+[compat]
+julia = "1.3"

README.md

@@ -67,9 +67,9 @@ Q
 
 ### History of this package
 
-`CatReps` was originally meant to wrap [Peter Webb](https://www-users.math.umn.edu/~webb/)'s pre-package [`catreps`](https://www-users.math.umn.edu/~webb/GAPfiles/catreps) into the categorical framework offered by [`CAP`](https://homalg-project.github.io/CAP_project/). The only dependency left can be found in the file [gap/catreps.g](https://codecov.io/gh/homalg-project/CatReps/src/master/gap/catreps.g). The entire functionality of [`catreps`](https://www-users.math.umn.edu/~webb/GAPfiles/catreps) is now available through [`FunctorCategories`](https://github.com/homalg-project/FunctorCategories).
+`CatReps` was originally meant to wrap [Peter Webb](https://www-users.math.umn.edu/~webb/)'s pre-package [`catreps`](https://www-users.math.umn.edu/~webb/GAPfiles/catreps) into the categorical framework offered by [`CAP`](https://homalg-project.github.io/docs/CAP_project/). The only dependency left can be found in the file [gap/catreps.g](https://codecov.io/gh/homalg-project/CatReps/src/master/gap/catreps.g). The entire functionality of [`catreps`](https://www-users.math.umn.edu/~webb/GAPfiles/catreps) is now available through [`FunctorCategories`](https://homalg-project.github.io/pkg/FunctorCategories).
 
-In March 2020 [Peter Webb](https://www-users.math.umn.edu/~webb/)' and his coauthors made a major new release of the former packages `reps` and `catreps` in which they are combined as one. The code of these former packages is still available at [`groupreps`](https://www-users.math.umn.edu/~webb/GAPfiles/groupreps) ([manual](https://www-users.math.umn.edu/~webb/GAPfiles/grouprepstutorial.html)) (the new name for the former reps) and [`catreps`](https://www-users.math.umn.edu/~webb/GAPfiles/catreps) ([manual](https://www-users.math.umn.edu/~webb/GAPfiles/catrepstutorial.html)), but it will no longer be supported. The new package [`reps`](https://www-users.math.umn.edu/~webb/GAPfiles/reps) combines the functionality of both former packages.
+In March 2020 [Peter Webb](https://www-users.math.umn.edu/~webb/)' and his coauthors made a major new release of the former packages `reps` and `catreps` in which they are combined as one. The code of these former packages is still available at [`groupreps`](https://www-users.math.umn.edu/~webb/GAPfiles/groupreps) ([tutorial](https://www-users.math.umn.edu/~webb/GAPfiles/grouprepstutorial.html)) (the new name for the former reps) and [`catreps`](https://www-users.math.umn.edu/~webb/GAPfiles/catreps) ([tutorial](https://www-users.math.umn.edu/~webb/GAPfiles/catrepstutorial.html)), but it will no longer be supported. The new package [`reps`](https://www-users.math.umn.edu/~webb/GAPfiles/reps) combines the functionality of both former packages.
 
 <!-- BEGIN FOOTER -->
 [docs-img]: https://img.shields.io/badge/docs-stable-blue.svg

examples/CategoryOfRepresentations.g

@@ -18,7 +18,7 @@ SetIsLinearClosureOfACategory( kq, true );
 #! A representation of the category c3c3 is another way to encode
 #! a module homomorphism between two modules over the cyclic group $C_3$ of order $3$:
 #! The vector space underlying the first module is the given by the value of (1).
-#! The action of C3 on the first module is given by the value of (a).
+#! The action of $C_3$ on the first module is given by the value of (a).
 #! The vector space underlying the second module is the given by the value of (2).
 #! The action on the second module is given by the value of (c).
 #! The above relation of the quiver states that the value of (b) is
@@ -65,9 +65,9 @@ Display( zero );
 #! (an empty 0 x 0 matrix)
 #! 
 #! A zero, identity morphism in Category of matrices over GF(3)
-const := TensorUnit( CatReps );
+unit := TensorUnit( CatReps );
 #! <(1)->1, (2)->1; (a)->1x1, (b)->1x1, (c)->1x1>
-Display( const );
+Display( unit );
 #! An object in The category of functors: Algebroid generated by the
 #! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
 #! over GF(3) defined by the following data:
@@ -139,13 +139,13 @@ Display( nine );
 #!  . . . 1
 #! 
 #! A morphism in Category of matrices over GF(3)
-nine(kq.1);
+nine( kq.1 );
 #! <A vector space object over GF(3) of dimension 5>
-nine(kq.2);
+nine( kq.2 );
 #! <A vector space object over GF(3) of dimension 4>
-nine(kq.b);
+nine( kq.b );
 #! <A morphism in Category of matrices over GF(3)>
-Display( nine(kq.b) );
+Display( nine( kq.b ) );
 #!  . 1 . .
 #!  . . 1 .
 #!  . . . .
@@ -165,11 +165,11 @@ fortyone( kq.1 );
 #! <A vector space object over GF(3) of dimension 25>
 fortyone( kq.2 );
 #! <A vector space object over GF(3) of dimension 16>
-fortyone(kq.a) = TensorProductOnMorphisms( nine(kq.a), nine(kq.a) );
+fortyone( kq.a ) = TensorProductOnMorphisms( nine( kq.a ), nine( kq.a ) );
 #! true
-fortyone(kq.b) = TensorProductOnMorphisms( nine(kq.b), nine(kq.b) );
+fortyone( kq.b ) = TensorProductOnMorphisms( nine( kq.b ), nine( kq.b ) );
 #! true
-fortyone(kq.c) = TensorProductOnMorphisms( nine(kq.c), nine(kq.c) );
+fortyone( kq.c ) = TensorProductOnMorphisms( nine( kq.c ), nine( kq.c ) );
 #! true
 Display( fortyone );
 #! An object in The category of functors: Algebroid generated by the
@@ -271,8 +271,6 @@ iso := UniversalMorphismFromDirectSum( etas );
 #! <(1)->25x25, (2)->16x16>
 IsIsomorphism( iso );
 #! true
-iso;
-#! <(1)->25x25, (2)->16x16>
 Display( Source( iso ) );
 #! An object in The category of functors: Algebroid generated by the
 #! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
@@ -459,7 +457,7 @@ Display( six );
 #!  . . 1
 #! 
 #! A morphism in Category of matrices over GF(3)
-emb := EmbeddingOfSumOfImagesOfAllMorphisms( const, six );
+emb := EmbeddingOfSumOfImagesOfAllMorphisms( unit, six );
 #! <(1)->1x3, (2)->0x3>
 Display( emb );
 #! A morphism in The category of functors: Algebroid generated by the
@@ -509,17 +507,17 @@ Display( s1 );
 #! A zero, isomorphism in Category of matrices over GF(3)
 kqop := AlgebroidOverOppositeAlgebra( kq );
 #! Algebroid generated by the right quiver q_op(2)[a:1->1,b:2->1,c:2->2]
-Y := YonedaEmbedding( kqop );
+Yop := YonedaEmbedding( kqop );
 #! Yoneda embedding functor
-Display( Y );
+Display( Yop );
 #! Yoneda embedding functor:
 #! 
 #! Algebroid generated by the right quiver q_op(2)[a:1->1,b:2->1,c:2->2]
 #!   |
 #!   V
 #! The category of functors: Algebroid generated by the right quiver
 #! q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices over GF(3)
-proj1 := Y( kqop.1 );
+proj1 := Yop( kqop.1 );
 #! <(1)->3, (2)->3; (a)->3x3, (b)->3x3, (c)->3x3>
 IsProjective( proj1 );
 #! true
@@ -557,7 +555,7 @@ Display( proj1 );
 #!  1 . .
 #! 
 #! A morphism in Category of matrices over GF(3)
-e1 := EmbeddingOfSumOfImagesOfAllMorphisms( const, proj1 );
+e1 := EmbeddingOfSumOfImagesOfAllMorphisms( unit, proj1 );
 #! <(1)->1x3, (2)->1x3>
 Source( e1 );
 #! <(1)->1, (2)->1; (a)->1x1, (b)->1x1, (c)->1x1>
@@ -597,17 +595,30 @@ Display( five );
 #!  . . 1
 #! 
 #! A morphism in Category of matrices over GF(3)
+#! @EndExample
+#!  The next calculation shows that the $3$-dimensional representation of $C_3$
+#!  associated to object $1$ is a single copy of the regular representation of $C_3$.
+#! @Example
 SumOfImagesOfAllMorphisms( s1, six );
 #! <(1)->1, (2)->0; (a)->1x1, (b)->1x0, (c)->0x0>
+#! @EndExample
+#!  The next calculation shows that the quotient representation <C>five</C> maps
+#!  its module at object $1$ monomorphically to the module at object $2$,
+#!  which must either be indecomposable of dimension $3$, or else the
+#!  direct sum of indecomposables of dimension $2$ and $1$.
+#! @Example
 SumOfImagesOfAllMorphisms( s1, five );
 #! <(1)->0, (2)->0; (a)->0x0, (b)->0x0, (c)->0x0>
-SumOfImagesOfAllMorphisms( const, five );
+SumOfImagesOfAllMorphisms( unit, five );
 #! <(1)->1, (2)->1; (a)->1x1, (b)->1x1, (c)->1x1>
-SumOfImagesOfAllMorphisms( five, const );
-#! <(1)->0, (2)->1; (a)->0x0, (b)->0x1, (c)->1x1>
-SumOfImagesOfAllMorphisms( six, const );
+#! @EndExample
+#!  The next calculation shows that the module at object $2$ for <C>six</C>
+#!  is indecomposable of dimension $3$.
+#!  We now have sufficient information to describe <C>six</C> completely.
+#! @Example
+SumOfImagesOfAllMorphisms( six, unit );
 #! <(1)->0, (2)->1; (a)->0x0, (b)->0x1, (c)->1x1>
-proj2 := Y( kqop.2 );
+proj2 := Yop( kqop.2 );
 #! <(1)->0, (2)->3; (a)->0x0, (b)->0x3, (c)->3x3>
 IsProjective( proj2 );
 #! true

examples/julia/notebooks/.gitignore

@@ -0,0 +1,2 @@
+/.ipynb_checkpoints/
+/Manifest.toml