In a domain and in categories referenced in a domain the notation % represents "this domain" (or self in some programming languages). So we commonly write for example:

  with
    f: (%,%) -> %

to indicate a function f which takes a pair of values in this domain and returns a value in this same domain - whatever domain we happen to be talking about in this context.

But what if we are interested in the domain as a functor? Suppose I was writing an "endofunctor" domain constructor like Set and I wanted to treat constructions like Set Set R, i.e. sets of sets as something special. E.g.

--)abbrev domain MYSET MySet
#pile
#include "axiom"
MonadCat(T:SetCategory,M:SetCategory->SetCategory):Category == with
  join: M M T -> M T

MySet(T:SetCategory): Join(MonadCat(T,MySet),SetAggregate(T)) with
     finiteAggregate
     --join: MySet MySet T -> MySet T
   == add
     Rep == List T
     --rep(x:%):Rep == x pretend Rep
     --per(x:Rep):% == x pretend %

     Rep2 == List List T
     rep2(x:MySet MySet T):Rep2 == x pretend Rep2
     per2(x:Rep2):MySet MySet T == x pretend MySet MySet T

     coerce(x:%):OutputForm ==
       brace(map(coerce$T, rep x)$ListFunctions2(T,OutputForm))
     ((x:%) = (y:%)):Boolean == (rep(x) = rep(y))$Rep
     construct(x:List T):% == per(removeDuplicates(x)$Rep)
     parts(x:%):List T == rep x
     join(x:MySet MySet T):MySet T ==
       construct(concat(rep2 x)$List(T))$%

     copy(x:%):% == per(copy(rep x)$Rep)
     empty():% == per(empty()$Rep)
     map(f:T->T,x:%):% == per(map(f,rep x)$Rep)
     brace():% == empty()$%
     brace(x:List(T)):% == construct(x)$%
     set():% == empty()$%
     set(x:List(T)):% == construct(x)$%

     -- dummy exports as required by Aldor
     _<(x:%, y:%):Boolean == true
     intersect(x:%, y:%):% == empty()$%
     difference(x:%, y:%):% == empty()$%
     subset?(x:%, y:%):Boolean == true
     union(x:%, y:%):% == empty()$%
     if T has ConvertibleTo(InputForm) then
       convert(x:%):InputForm == convert(rep(x))$Rep

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8835079522190382419-25px001.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.
#1 (Warning) Could not use archive file `libaxiom.al'.
#2 (Warning) Could not use archive file `libaxiom.al'.
"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 4: 
import from AxiomLib;
............^
[L4 C13] #3 (Error) No meaning for identifier `AxiomLib'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 15: 
import { true: %, false: % } from Boolean;
..................................^
[L15 C35] #4 (Error) No meaning for identifier `Boolean'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 17: 
        string:         Literal -> %;
........................^.......^
[L17 C25] #5 (Error) No meaning for identifier `Literal'.
[L17 C33] #6 (Error) There are no suitable meanings for the operator `->'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 18: 
} from String;
.......^
[L18 C8] #8 (Error) No meaning for identifier `String'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8835079522190382419-25px001.as", line 4: 
MonadCat(T:SetCategory,M:SetCategory->SetCategory):Category == with
.........^.^........................^
[L4 C10] #12 (Error) Have determined 1 possible types for the expression.
        Meaning 1: ?, ?
  The context requires an expression of type Tuple(Type).
[L4 C12] #9 (Error) No meaning for identifier `SetCategory'.
[L4 C37] #10 (Error) There are no suitable meanings for the operator `->'.
[L4 C37] #13 (Fatal Error) Too many errors (use `-M emax=n' or `-M no-emax' to change the limit).

   The )library system command was not called after compilation.

)sh MySet

   The )show system command is used to display information about types 
      or partial types. For example, )show Integer will show 
      information about Integer .

      MySet is not the name of a known type constructor. If you want to
      see information about any operations named MySet , issue
                          )display operations MySet 

)di op join

There are 2 unexposed functions called join :
   [1] (JetDifferentialEquation(D1,D2),JetDifferentialEquation(D1,D2))
             -> JetDifferentialEquation(D1,D2)
            from JetDifferentialEquation(D1,D2)
            if D1 has JBC and D2 has JBFC(D1)
   [2] (SparseEchelonMatrix(D1,D2),SparseEchelonMatrix(D1,D2)) -> 
            SparseEchelonMatrix(D1,D2)
            from SparseEchelonMatrix(D1,D2)
            if D1 has ORDSET and D2 has RING

MySet(Integer) has MonadCat(Integer,MySet)

   There are no library operations named MySet 
      Use HyperDoc Browse or issue
                               )what op MySet
      to learn if there is any operation containing " MySet " in its 
      name.

   Cannot find a definition or applicable library operation named MySet
      with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

m1:MySet(Integer) := construct([1,2,3])$MySet(Integer)

   There are no library operations named MySet 
      Use HyperDoc Browse or issue
                               )what op MySet
      to learn if there is any operation containing " MySet " in its 
      name.

   Cannot find a definition or applicable library operation named MySet
      with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
m2:MySet(Integer) := construct([4,5,6])$MySet(Integer)

   There are no library operations named MySet 
      Use HyperDoc Browse or issue
                               )what op MySet
      to learn if there is any operation containing " MySet " in its 
      name.

   Cannot find a definition or applicable library operation named MySet
      with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
ml:=[m1,m2]

(1)

mm:MySet MySet Integer := construct([m1,m2])$MySet(MySet(Integer))

   There are no library operations named MySet 
      Use HyperDoc Browse or issue
                               )what op MySet
      to learn if there is any operation containing " MySet " in its 
      name.

   Cannot find a definition or applicable library operation named MySet
      with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
join mm

   There are no exposed library operations named join but there are 2 
      unexposed operations with that name. Use HyperDoc Browse or issue
                              )display op join
      to learn more about the available operations.

   Cannot find a definition or applicable library operation named join 
      with argument type(s) 
                                Variable(mm)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.