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Is it possible to modify the style of the arrows in a 2-cell in xy?

\documentclass{standalone}
\usepackage{amsmath,amssymb,amsfonts}
 \usepackage[all,2cell]{xy}
 \UseAllTwocells
\begin{document}
\xymatrix{
&B \ar[d]^g\dllowertwocell^{fg}_{1}{\epsilon} \\
B \ar[r]_g  \ar[ur] & A
}

\end{document}

I would like the codomain of \epsilon to be drawn as an identity, since it is one. \dllowertwocell@{=}^{fg}_{1}{\epsilon} has, of course, no effect since it is impossible to tell xy which arrow must be modified. Also, even the command that says at which point to put the label (let's say \ar[r]^(.25){f}) doesn't work.

enter image description here

fosco
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