Is there a name to this math structure?

gistfile1.md

D is a product of T but non-commutative

T x T -> D

but

T1 x T2 != T2 x T1

From product D, we can uniquely extract the original 2 T

D -> T x T

So globally, there is an isomorphism

T x T <-> D

D is a monoid

• with an op + (associative but non-commutative)

D + D -> D

• an id element E

D + E = E + D = D

To be complete:

• T represents the set of RoseTrees
• D represents a Diff between 2 rosetrees