was introduced in the general setting of monoidal dagger categories by Coecke and Pavlovi[ć]{} in [@coeckepavlovic:classicalobjects]. In their version, a *dagger Frobenius structure* on an object $A$ in a dagger monoidal category is a commutative comonoid $(\xymatrix@1{I & A \ar|-{\varepsilon}[l] \ar|-{\delta}[r] & A {\ensuremath{\otimes}}A})$ satisfying certain additional equations: $$\begin{aligned}
      ({\ensuremath{\mathrm{id}_{A}}} \otimes \delta) {\circ}\delta 
  & = (\delta \otimes {\ensuremath{\mathrm{id}_{A}}}) {\circ}\delta, \tag{A} \\
      ({\ensuremath{\mathrm{id}_{A}}} {\ensuremath{\otimes}}\varepsilon) {\circ}\delta 
  & = {\ensuremath{\mathrm{id}_{A}}}, \tag{U} \\
      \sigma {\circ}\delta 
  & = \delta, \tag{C} \\
      \delta^\dag {\circ}\delta 
  & = {\ensuremath{\mathrm{id}_{A}}}, \tag{M} \\
      \delta{\circ}\delta^\dag 
  & = (\delta^\dag {\ensuremath{\otimes}}{\ensuremath{\mathrm{id}_{A}}}) {\circ}({\ensuremath{\mathrm{id}_{A}}} {\ensuremath{\otimes}}\delta). \tag{F}\end{aligned}$$ These equations become more perspicuous when represented diagrammatically, as below. Here, we draw the comultiplication $\delta$ as $\vcenter{\hbox{{
 \begin{tikzpicture}[scale=0.2]  \PandocStartInclude{tikz/comultiplication.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}}}$, and the counit $\varepsilon$ as $\vcenter{\hbox{{
 \begin{tikzpicture}[scale=0.2]  \PandocStartInclude{tikz/counit.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}}}$. $${
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/A-lhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}} \; \stackrel{\text{(A)}}{=} \; {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/A-rhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}
  \qquad\qquad\qquad
  {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/U-lhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}} \; \stackrel{\text{(U)}}{=} \; {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/U-rhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}
  \qquad\qquad\qquad
  {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/C-lhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}} \; \stackrel{\text{(C)}}{=} \; {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/C-rhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}$$ $${
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/M-lhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}} \; \stackrel{\text{(M)}}{=} \; {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/M-rhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}
  \qquad\qquad\qquad
  {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/F-lhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}} \; \stackrel{\text{(F)}}{=} \; {
 \begin{tikzpicture}[]  \PandocStartInclude{tikz/F-rhs.tikz}\PandocEndInclude{input}{24}{23} \end{tikzpicture}}$$ A ‘right-handed version’ of the Frobenius law (F) follows from (C); in the noncommutative case we should add this symmetric version 