diff --git a/src/blocktensor.jl b/src/blocktensor.jl
index 5b9f421..859957a 100644
--- a/src/blocktensor.jl
+++ b/src/blocktensor.jl
@@ -322,11 +322,21 @@ function Base.convert(::Type{<:AbstractTensorMap{S,N₁,N₂}}, t::BlockTensorMa
     return tdst
 end
 
+# Utility
+# -------
+
+function Base.copy(t::BlockTensorMap{S,N₁,N₂,T,N}) where {S,N₁,N₂,T,N}
+    return BlockTensorMap{S,N₁,N₂,T,N}(copy(t.data), codomain(t), domain(t))
+end
+function Base.deepcopy(t::BlockTensorMap{S,N₁,N₂,T,N}) where {S,N₁,N₂,T,N}
+    return BlockTensorMap{S,N₁,N₂,T,N}(deepcopy(t.data), codomain(t), domain(t))
+end
+
 # TensorKit Interface
 # -------------------
 
-TK.spacetype(::Union{T,Type{T}}) where {S,T<:BlockTensorMap{S}} = S
-function TK.sectortype(::Union{T,Type{T}}) where {S,T<:BlockTensorMap{S}}
+TK.spacetype(::Union{T,Type{<:T}}) where {S,T<:BlockTensorMap{S}} = S
+function TK.sectortype(::Union{T,Type{<:T}}) where {S,T<:BlockTensorMap{S}}
     return sectortype(S)
 end
 TK.storagetype(::Union{B,Type{B}}) where {T,B<:BlockTensorArray{T}} = storagetype(T)
@@ -338,9 +348,7 @@ TK.similarstoragetype(t::BlockTensorMap, T) = TK.similarstoragetype(typeof(t), T
 
 TK.numout(::Union{T,Type{T}}) where {S,N₁,T<:BlockTensorMap{S,N₁}} = N₁
 TK.numin(::Union{T,Type{T}}) where {S,N₁,N₂,T<:BlockTensorMap{S,N₁,N₂}} = N₂
-function TK.numind(::Union{T,Type{T}}) where {S,N₁,N₂,T<:BlockTensorMap{S,N₁,N₂}}
-    return N₁ + N₂
-end
+TK.numind(::Union{T,Type{T}}) where {S,N₁,N₂,T<:BlockTensorMap{S,N₁,N₂}} = N₁ + N₂
 
 TK.codomain(t::BlockTensorMap) = t.codom
 TK.domain(t::BlockTensorMap) = t.dom
@@ -591,9 +599,6 @@ function VI.inner(x::BlockTensorMap, y::BlockTensorMap)
     return s
 end
 
-# TODO: this is type-piracy!
-# VI.scalartype(::Type{Union{A,B}}) where {A,B} = Union{scalartype(A), scalartype(B)}
-
 # TensorOperations
 # ----------------
 
@@ -767,6 +772,41 @@ function TO.tensorstructure(t::BlockTensorMap, iA::Int, conjA::Symbol)
     return conjA == :N ? space(t, iA) : conj(space(t, iA))
 end
 
+function TO.tensorcontract_structure(pC::Index2Tuple{N₁,N₂},
+                                     A::BlockTensorMap{S}, pA::Index2Tuple, conjA::Symbol,
+                                     B::BlockTensorMap{S}, pB::Index2Tuple,
+                                     conjB::Symbol) where {S,N₁,N₂}
+    spaces1 = TO.flag2op(conjA).(space.(Ref(A), pA[1]))
+    spaces2 = TO.flag2op(conjB).(space.(Ref(B), pB[2]))
+    spaces = (spaces1..., spaces2...)
+    cod = ProductSumSpace{S,N₁}(getindex.(Ref(spaces), pC[1]))
+    dom = ProductSumSpace{S,N₂}(dual.(getindex.(Ref(spaces), pC[2])))
+    return dom → cod
+end
+function TO.tensorcontract_structure(pC::Index2Tuple{N₁,N₂},
+                                     A::BlockTensorMap{S}, pA::Index2Tuple, conjA::Symbol,
+                                     B::AbstractTensorMap{S}, pB::Index2Tuple,
+                                     conjB::Symbol) where {S,N₁,N₂}
+    spaces1 = TO.flag2op(conjA).(space.(Ref(A), pA[1]))
+    spaces2 = TO.flag2op(conjB).(space.(Ref(B), pB[2]))
+    spaces = (spaces1..., spaces2...)
+    cod = ProductSumSpace{S,N₁}(getindex.(Ref(spaces), pC[1]))
+    dom = ProductSumSpace{S,N₂}(dual.(getindex.(Ref(spaces), pC[2])))
+    return dom → cod
+end
+function TO.tensorcontract_structure(pC::Index2Tuple{N₁,N₂},
+                                     A::AbstractTensorMap{S}, pA::Index2Tuple,
+                                     conjA::Symbol,
+                                     B::BlockTensorMap{S}, pB::Index2Tuple,
+                                     conjB::Symbol) where {S,N₁,N₂}
+    spaces1 = TO.flag2op(conjA).(space.(Ref(A), pA[1]))
+    spaces2 = TO.flag2op(conjB).(space.(Ref(B), pB[2]))
+    spaces = (spaces1..., spaces2...)
+    cod = ProductSumSpace{S,N₁}(getindex.(Ref(spaces), pC[1]))
+    dom = ProductSumSpace{S,N₂}(dual.(getindex.(Ref(spaces), pC[2])))
+    return dom → cod
+end
+
 function TO.checkcontractible(tA::BlockTensorMap{S}, iA::Int, conjA::Symbol,
                               tB::BlockTensorMap{S}, iB::Int, conjB::Symbol,
                               label) where {S}
@@ -780,6 +820,18 @@ end
 # PlanarOperations
 # ----------------
 
+function TK.BraidingTensor(V1::SumSpace{S}, V2::SumSpace{S}) where {S}
+    tdst = BlockTensorMap{S,2,2,TK.BraidingTensor{S,Matrix{ComplexF64}}}(undef, V2 ⊗ V1, V1 ⊗ V2)
+    for I in CartesianIndices(tdst)
+        if I[1] == I[4] && I[2] == I[3]
+            V = getsubspace(space(tdst), I)
+            @assert domain(V)[2] == codomain(V)[1] && domain(V)[1] == codomain(V)[2]
+            tdst[I] = TK.BraidingTensor(V[2], V[1])
+        end
+    end
+    return tdst
+end
+
 function TK.planaradd!(C::BlockTensorMap{S,N₁,N₂},
                        A::BlockTensorMap{S},
                        p::Index2Tuple{N₁,N₂},
@@ -955,17 +1007,7 @@ for (T1, T2) in
                                           convert(BlockTensorMap, B), pB, conjB)
         end
         
-        @eval function TO.tensorcontract_structure(pC::Index2Tuple{N₁,N₂}, A::$T1{S},
-                                             pA::Index2Tuple, conjA::Symbol,
-                                             B::$T2{S},
-                                             pB::Index2Tuple, conjB::Symbol) where {S,N₁,N₂}
-            spaces1 = TO.flag2op(conjA).(space.(Ref(A), pA[1]))
-            spaces2 = TO.flag2op(conjB).(space.(Ref(B), pB[2]))
-            spaces = (spaces1..., spaces2...)
-            cod = ProductSumSpace{S,N₁}(getindex.(Ref(spaces), pC[1]))
-            dom = ProductSumSpace{S,N₂}(dual.(getindex.(Ref(spaces), pC[2])))
-            return dom → cod
-        end
+        
     end
 
     if !(T1 === :BlockTensorMap && T2 === :BlockTensorMap)