objects $X,Y$ of ${\mathcal{S}}$, the notation $X \simeq Y$ means that $X$ and $Y$ are isomorphic, i.e., that there is an invertible morphism $X\to Y$.

Conventions {#sect-conventions}
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We will suppress in our formulas the associativity and unitality constraints of the monoidal category ${\mathcal{S}}$. This does not lead to ambiguity because by Mac Lane’s coherence theorem (see [@ML]), all legitimate ways of inserting these constraints give the same results. For any objects $X_1,...,X_n$ with $n\geq 2$, we set $$X_1 \otimes X_2 \otimes \cdots \otimes X_n=(... ((X_1\otimes X_2) \otimes X_3) \otimes
\cdots \otimes X_{n-1}) \otimes X_n$$ and similarly for morphisms.

Graphical conventions
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Morphisms in ${\mathcal{S}}$ may be represented by diagrams to be read from bottom to top. We discuss here the basics of this Penrose graphical calculus. The identity ${\mathrm{id}}_X$ of an object $X$ of ${\mathcal{S}}$, a morphism $f{\colon}X \to Y$ in ${\mathcal{S}}$, and the composition of two morphisms $f{\colon}X \to Y$ and $g{\colon}Y \to Z$ may be graphically represented as follows: $$\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X$}} \psfrag{Y}[Bc][Bc]{\scalebox{.8}{$Y$}} \psfrag{h}[Bc][Bc]{\scalebox{.9}{$f$}} \psfrag{g}[Bc][Bc]{\scalebox{.9}{$g$}}
\psfrag{Z}[Bc][Bc]{\scalebox{.8}{$Z$}} {\mathrm{id}}_X=\, {\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{identitymorph-bt.eps}}}}\,,\quad f=\, {\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{morphism-bt.eps}}}}\;\,,\quad \text{and} \quad gf=\, {\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{morphismcompo-bt.eps}}}}\,\; .$$ The monoidal product of two morphisms $f{\colon}X \to Y$ and $g {\colon}U \to V$ in ${\mathcal{S}}$ is represented by juxtaposition: $$\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X$}}
\psfrag{h}[Bc][Bc]{\scalebox{.9}{$f$}}
\psfrag{Y}[Bl][Bl]{\scalebox{.8}{$Y$}}
f\otimes 