g= \,{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{morphism-bt.eps}}}}\,
\psfrag{X}[Bl][Bl]{\scalebox{.8}{$U$}}
\psfrag{g}[Bc][Bc]{\scalebox{.9}{$g$}}
\psfrag{Y}[Bl][Bl]{\scalebox{.8}{$V$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{morphism3-bt.eps}}}}\,\;   .$$ We can also use boxes with several strands attached to their horizontal sides. For example, a morphism $f {\colon}X \otimes Y \to A \otimes B \otimes C$ with $X,Y,A,B,C\in {\mathrm{Ob}}({\mathcal{S}})$ may be represented in various ways, such as $$\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X$}}
\psfrag{h}[Bc][Bc]{\scalebox{.9}{$f$}}
\psfrag{Y}[Bl][Bl]{\scalebox{.8}{$Y$}}
\psfrag{A}[Bl][Bl]{\scalebox{.8}{$A$}}
\psfrag{B}[Bl][Bl]{\scalebox{.8}{$B$}}
\psfrag{C}[Bl][Bl]{\scalebox{.8}{$C$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{ex-penro1.eps}}}}
\qquad \text{or} \qquad
\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X \otimes Y$}}
\psfrag{h}[Bc][Bc]{\scalebox{.9}{$f$}}
\psfrag{A}[Bl][Bl]{\scalebox{.8}{$A$}}
\psfrag{B}[Bl][Bl]{\scalebox{.8}{$B \otimes C$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{ex-penro2c.eps}}}}
\qquad \text{or} \qquad
\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X$}}
\psfrag{h}[Bc][Bc]{\scalebox{.9}{$f$}}
\psfrag{Y}[Bl][Bl]{\scalebox{.8}{$Y$}}
\psfrag{A}[Br][Br]{\scalebox{.8}{$A \otimes B$}}
\psfrag{B}[Bl][Bl]{\scalebox{.8}{$C$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{ex-penro2b.eps}}}} \,\;.$$ In accordance with conventions of Section \[sect-conventions\], we ignore here the associativity constraint between the objects $A \otimes B \otimes C =(A \otimes B)\otimes C$ and $A \otimes (B\otimes C)$. A box whose lower/upper side has no attached strands represents a morphism with source/target ${\mathbb{1}}$. For example, morphisms $\alpha{\colon}{\mathbb{1}}\to {\mathbb{1}}$, $\beta{\colon}{\mathbb{1}}\to X$, $\gamma{\colon}X \to {\mathbb{1}}$ with $X\in {\mathrm{Ob}}({\mathcal{S}})$ may be represented by the diagrams $$\psfrag{h}[Bc][Bc]{\scalebox{.9}{$\alpha$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{ex-penro5.eps}}}}\;, \qquad
\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X$}}
\psfrag{h}[Bc][Bc]{\scalebox{.9}{$\beta$}}
\psfrag{Y}[Bl][Bl]{\scalebox{.8}{$Y$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{ex-penro3b.eps}}}}\;, \qquad
\psfrag{X}[Bl][Bl]{\scalebox{.8}{$X$}}
\psfrag{h}[Bc][Bc]{\scalebox{.9}{$\gamma$}}
\psfrag{Y}[Bl][Bl]{\scalebox{.8}{$Y$}}
{\raisebox{-.45\height}{\scalebox{.9}{\includegraphics{ex-penro4b.eps}}}}\;.$$

Every diagram which is ${\mathcal{S}}$-colored as above determines a morphism in ${\mathcal{S}}$ obtained as follows. First slice the diagram into horizontal strips so that each strip is made of juxtaposition of vertical segments or boxes. Then, for each strip, take the monoidal product of the morphisms associated to 