diff --git a/src/linalg/linalg.jl b/src/linalg/linalg.jl
index aedc2bb..0abd9a3 100644
--- a/src/linalg/linalg.jl
+++ b/src/linalg/linalg.jl
@@ -129,8 +129,14 @@ const _TM_CAN_MUL = Union{
     TensorMap, AdjointTensorMap{<:Any, <:Any, <:Any, <:Any, <:TensorMap}, BraidingTensor,
 }
 function _mul!!(C::_TM_CAN_MUL, A::_TM_CAN_MUL, B::_TM_CAN_MUL, α::Number, β::Number)
-    return mul!(C, A, B, α, β)
+    return mul!(C, A, B, _blasscalar(α), _blasscalar(β))
 end
+
+# `LinearAlgebra` cannot handle `One`/`Zero`, which carry the same meaning as `true`/`false`
+# TODO: remove once `VectorInterface` implements the full `Number` interface for these
+_blasscalar(α::Number) = α
+_blasscalar(::One) = true
+_blasscalar(::Zero) = false
 # TODO: optimize other implementations
 
 # ensure that mixes with AbstractBlockTensorMap and AbstractTensorMap behave as expected:
diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index b4d97a4..8415b62 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -128,9 +128,10 @@ end
 function TensorKit._sectors(S::SumSpace, ::Type{I}) where {I}
     s = Set{I}()
     for v in S.spaces
-        s = s ∪ sectors(v)
+        union!(s, sectors(v))
     end
-    return values(s)
+    # sorted for a canonical order, consistent with `GradedSpace` and `blocksectors`
+    return sort!(collect(s))
 end
 
 TensorKit.dim(S::SumSpace, sector::Sector) = sum(v -> dim(v, sector), S.spaces; init = 0)
diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index e4faa52..1c877ba 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -129,6 +129,7 @@ end
 
     @test @constinferred(sectortype(V)) == sectortype(V1)
     @test ((@constinferred sectors(V))...,) == (U1Irrep(0), U1Irrep(1))
+    @test issorted(sectors(V))
     @test length(sectors(V)) == 2
     @test @constinferred(hassector(V, U1Irrep(0)))
     @test !@constinferred(hassector(V, U1Irrep(2)))
@@ -188,7 +189,8 @@ end
     @test unitspace(V) == unitspace(V1)
 
     @test @constinferred(sectortype(V)) == sectortype(V1)
-    @test ((@constinferred sectors(V))...,) == (C1, C0, D1, D0, M) # ordering matters
+    @test ((@constinferred sectors(V))...,) == (C0, C1, M, D0, D1) # sorted order
+    @test issorted(sectors(V))
     @test length(sectors(V)) == 5
     @test @constinferred(hassector(V, M))
     @test !@constinferred(hassector(V, Mop))