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  2 Category of Categories
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  Categories  itself  with  functors as morphisms form a category. So the data
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  structure  of  CapCategorys  is  designed  to be objects in a category. This
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  category  is  implemented  in  CapCat. For every category, the corresponding
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  object  in  Cat  can  be  obtained via AsCatObject. The implemetation of the
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  category  of  categories  offers  a  data  structure for functors. Those are
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  implemented  as  morphisms in this category, so functors can be handled like
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  morphisms  in  a category. Also convenience functions to install functors as
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  methods are implemented (in order to avoid ApplyFunctor).
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  2.1 The Category Cat
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  2.1-1 CapCat
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  CapCat global variable
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  This  variable  stores  the category of categories. Every category object is
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  constructed  as  an  object  in  this  category,  so Cat is constructed when
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  loading the package.
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  2.2 Categories
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  2.2-1 IsCapCategoryAsCatObject
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  IsCapCategoryAsCatObject( object )  filter
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  Returns:  true or false
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  The GAP category of CAP categories seen as object in Cat.
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  2.2-2 IsCapFunctor
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  IsCapFunctor( object )  filter
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  Returns:  true or false
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  The GAP category of functors.
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  2.2-3 IsCapNaturalTransformation
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  IsCapNaturalTransformation( object )  filter
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  Returns:  true or false
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  The GAP category of natural transformations.
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  2.3 Constructors
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  2.3-1 AsCatObject
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  AsCatObject( C )  attribute
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  Given a CAP category C, this method returns the corresponding object in Cat.
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  For  technical  reasons,  the filter IsCapCategory must not imply the filter
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  IsCapCategoryObject.  For example, if InitialObject is applied to an object,
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  it  returns  the  initial  object  of  its  category.  If it is applied to a
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  category,  it  returns the initial object of the category. If a CAP category
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  would  be  a  category object itself, this would be ambiguous. So categories
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  must  be  wrapped in a CatObject to be an object in Cat. This method returns
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  the wrapper object. The category can be reobtained by AsCapCategory.
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  2.3-2 AsCapCategory
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  AsCapCategory( C )  attribute
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  For  an  object  C  in Cat, this method returns the underlying CAP category.
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  This  method is inverse to AsCatObject, i.e. AsCapCategory( AsCatObject( A )
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  ) = A.
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  2.4 Functors
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  Functors  are  morphisms  in Cat, thus they have source and target which are
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  categories. A multivariate functor can be constructed via a product category
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  as  source,  a  presheaf is constructed via the opposite category as source.
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  Moreover,  an  object  and a morphism function can be added to a functor, to
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  apply it to objects or morphisms in the source category.
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  2.4-1 CapFunctor
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  CapFunctor( name, A, B )  operation
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  CapFunctor( name, A, B )  operation
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  CapFunctor( name, A, B )  operation
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  CapFunctor( name, A, B )  operation
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  CapFunctor( name, A, B )  operation
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  CapFunctor( name, A, B )  operation
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  These  methods  construct a CAP functor, i.e. a morphism in Cat. Name should
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  be  an  unique  name  for  the  functor, it is also used when the functor is
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  installed  as  a method. A and B are source and target. Both can be given as
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  object in Cat or as category itself.
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  2.4-2 AddObjectFunction
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  AddObjectFunction( functor, function )  operation
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  This  operation  adds a function to the functor which can then be applied to
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  objects  in the source. The given function function has to take one argument
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  which  must  be  an  object  in  the  source  category  and  should return a
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  CapCategoryObject.  The  object  is  automatically added to the range of the
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  functor when it is applied to the object.
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  2.4-3 FunctorObjectOperation
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  FunctorObjectOperation( F )  attribute
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  Returns:  a GAP operation
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  The  argument  is a functor F. The output is the GAP operation realizing the
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  action of F on objects.
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  2.4-4 AddMorphismFunction
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  AddMorphismFunction( functor, function )  operation
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  This  operation  adds a function to the functor which can then be applied to
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  morphisms  in  the  source.  The  given  function function has to take three
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  arguments  A,  \tau,  B.  When the funtor functor is applied to the morphism
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  \tau,  A  is  the  result of functor applied to the source of \tau, B is the
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  result of functor applied to the range.
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  2.4-5 FunctorMorphismOperation
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  FunctorMorphismOperation( F )  attribute
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  Returns:  a GAP operation
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  The  argument  is a functor F. The output is the GAP operation realizing the
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  action of F on morphisms.
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  2.4-6 ApplyFunctor
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  ApplyFunctor( func, A )  function
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  Returns:  IsCapCategoryCell
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  Applies the functor func to the object or morphism A.
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  2.4-7 InstallFunctor
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  InstallFunctor( functor, method_name )  operation
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  TODO
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  2.4-8 IdentityFunctor
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  IdentityFunctor( category )  attribute
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  Returns:  a functor
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  Returns  the identity functor of the category cat viewed as an object in the
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  category of categories.
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  2.4-9 FunctorCanonicalizeZeroObjects
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  FunctorCanonicalizeZeroObjects( category )  attribute
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  Returns:  a functor
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  Returns  the  endofunctor  of  the  category  cat  with zero which maps each
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  (object  isomorphic  to  the)  zero  object to ZeroObject(cat) and to itself
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  otherwise. This functor is equivalent to the identity functor.
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  2.4-10 NaturalIsomorophismFromIdentityToCanonicalizeZeroObjects
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  NaturalIsomorophismFromIdentityToCanonicalizeZeroObjects( category )  attribute
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  Returns:  a natural transformation
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  Returns   the   natural   isomorphism   from   the   identity   functor   to
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  FunctorCanonicalizeZeroObjects(cat).
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  2.4-11 FunctorCanonicalizeZeroMorphisms
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  FunctorCanonicalizeZeroMorphisms( category )  attribute
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  Returns:  a functor
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  Returns the endofunctor of the category cat with zero which maps each object
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  to  itself,  each  morphism  ϕ to itself, unless it is congruent to the zero
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  morphism;  in  this  case it is mapped to ZeroMorphism(Source(ϕ), Range(ϕ)).
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  This functor is equivalent to the identity functor.
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  2.4-12 NaturalIsomorophismFromIdentityToCanonicalizeZeroMorphisms
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  NaturalIsomorophismFromIdentityToCanonicalizeZeroMorphisms( category )  attribute
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  Returns:  a natural transformation
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  Returns   the   natural   isomorphism   from   the   identity   functor   to
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  FunctorCanonicalizeZeroMorphisms(cat).
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  2.5 Natural transformations
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  2.5-1 Name
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  Name( arg )  attribute
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  Returns:  a string
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  As  every functor, every natural transformation has a name attribute. It has
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  to be a string and will be set by the Constructor.
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  2.5-2 NaturalTransformation
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  NaturalTransformation( [name, ]F, G )  operation
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  Returns:  a natural transformation
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  Constructs  a  natural transformation between the functors F:A \rightarrow B
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  and  G:A  \rightarrow B. The string name is optional, and, if not given, set
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  automatically from the names of the functors
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  2.5-3 AddNaturalTransformationFunction
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  AddNaturalTransformationFunction( N, func )  operation
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  Adds  the function (or list of functions) func to the natural transformation
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  N. The function or each function in the list should take three arguments. If
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  N:  F  \rightarrow  G,  the  arguments  should be F(A), A, G(A). The ouptput
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  should be a morphism, F(A) \rightarrow G(A).
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  2.5-4 ApplyNaturalTransformation
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  ApplyNaturalTransformation( N, A )  function
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  Returns:  a morphism
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  Given  a  natural  transformation  N:F  \rightarrow  G and an object A, this
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  function  should return the morphism F(A) \rightarrow G(A), corresponding to
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  N.
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  2.5-5 InstallNaturalTransformation
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  InstallNaturalTransformation( N, name )  operation
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  Installs  the  natural  transformation  N  as  operation with the name name.
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  Argument for this operation is an object, output is a morphism.
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  2.5-6 HorizontalPreComposeNaturalTransformationWithFunctor
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  HorizontalPreComposeNaturalTransformationWithFunctor( N, F )  operation
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  Returns:  a natural transformation
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  Computes the horizontal composition of the natural transformation N and
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  2.5-7 HorizontalPreComposeFunctorWithNaturalTransformation
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  HorizontalPreComposeFunctorWithNaturalTransformation( F, N )  operation
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  Returns:  a natural transformation
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  Computes  the  horizontal  composition  of  the  functor  F  and the natural
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  transformation N.
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