{{x,y},{x,z}}{{w,x},{w,z},{x,y}}

Iterated map on functions

Something like {{x,y},{x,z}} is a word in a free monoid

Every concrete hyperedge is a generator; rule gives equivalences between words [[ as a schema ]]

Operator algebra without nesting

{{x,y},{x,z}}{{w,x},{w,z},{x,y}}

#### lambdas

lambdas

Needs matching; not an ordinary lambda

{{x_,y_},{x_,z_}}Module[{w},{{w,x},{w,z},{x,y}}]

Deploy an armada of lambdas:

{{0,5},{1,2},{3,2},{4,1}}

Treat the list as curried

Function[{e,f},Function[{c,d},Function[{a,b},XXXX]]][l[l[l[l[XXXXX]]]]]

Possibly using parametrized types to do matches

#### category theory

category theory

[[f endofunctor on the powerset of ]]

[[equipped with a morphism on the category Set]]

Object is set of possible hyperedges;

Tuples[Range[3],2]

In[]:=

{{1,1},{1,2},{1,3},{2,1},{2,2},{2,3},{3,1},{3,2},{3,3}}

Out[]=

Subsets[%]

In[]:=

Out[]=

This object is a set of sets....

Morphism maps one set onto another

Can I enumerate models with category theory??

## [More]

[More]

#### Rule application is associative

Rule application is associative

Concatenation of strings has associativity

Concatenation of hypergraphs has associativity and commutativity [ identity element is empty hypergraph ]

(Not clear what rule application means...)

Commutative monoid

{f[a,b],f[c,d],XXXXX}