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docs/src/lib/fusiontrees.md

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```@meta
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CurrentModule = TensorKit
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```
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# Type hierarchy

docs/src/lib/sectors.md

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CurrentModule = TensorKit
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```
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## Type hierarchy

docs/src/lib/spaces.md

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```@meta
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## Type hierarchy

docs/src/lib/tensors.md

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```@meta
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## Type hierarchy

docs/src/man/indexmanipulations.md

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# [Index manipulations](@id s_indexmanipulations)
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```
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```@setup indexmanip
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using TensorKit
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using LinearAlgebra
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- [`braid`](@ref) is the most general: it accepts any permutation and requires a `levels` argument — a tuple of heights, one per index — that determines whether each index crosses over or under the others it has to pass.
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- [`permute`](@ref) is a simpler interface for sector types with a symmetric braiding (`BraidingStyle(I) isa SymmetricBraiding`), where over- and under-crossings are equivalent and `levels` is therefore not needed.
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- [`transpose`](@ref) is restricted to *cyclic* permutations (indices do not cross). Unlike `braid`, it introduces a compensating (inverse) twist to satisfy the categorical definition of transpose, as illustrated below:
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```@raw html
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<img src="../img/tensor-transpose.svg" alt="transpose" class="color-invertible"/>
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```
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- [`repartition`](@ref) only moves the codomain/domain boundary without reordering the indices at all.
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For plain tensors (`sectortype(t) == Trivial`), `permute` and `braid` act like `permutedims` on the underlying array:

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