TLIdentity[1] = {TLMono[0,1]**TLEpi[1,0]};
TLIdentity[n_/;n>1]:=TLIdentity[n] =  TLIdentity[1]⊗TLIdentity[n-1]

HalfClickRotation[X_]:= 
Module[{n=source[X],m=target[X], 
AMono = Flatten[PathsEndingAt[n,n]]⊗ TLMono[0,1,0], 
AEpi =TLEpi[0,1,0]⊗Flatten[PathsEndingAt[m,m]]
},
AMono**(TLIdentity[1]⊗X⊗TLIdentity[1])**AEpi
]

Rotation[X_] := HalfClickRotation[HalfClickRotation[X]]