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\[\begin{tikzcd}[ampersand replacement=\&,column sep=3.15em]
	{B''} \&\& {B''} \\
	{B'} \&\& {B''} \\
	{B'} \& {B'} \& {B''} \\
	B \& {B'} \& {B''}
	\arrow[""{name=0, anchor=center, inner sep=0}, "{p_{d'}}"', from=1-1, to=2-1]
	\arrow["\id"', from=2-1, to=3-1]
	\arrow[""{name=1, anchor=center, inner sep=0}, "{p_d}"', from=3-1, to=4-1]
	\arrow[""{name=2, anchor=center, inner sep=0}, "{\delrp_{d'}}", from=1-3, to=2-3]
	\arrow["\id", from=2-3, to=3-3]
	\arrow[""{name=3, anchor=center, inner sep=0}, "{\push_{d'}(\delrp_d)}", from=3-3, to=4-3]
	\arrow["{r(B'')}", "\shortmid"{marking}, no head, from=1-1, to=1-3]
	\arrow["{d'}", "\shortmid"{marking}, no head, from=2-1, to=2-3]
	\arrow["{r(B')}", "\shortmid"{marking}, no head, from=3-1, to=3-2]
	\arrow["{d'}", "\shortmid"{marking}, no head, from=3-2, to=3-3]
	\arrow["d"', "\shortmid"{marking}, no head, from=4-1, to=4-2]
	\arrow["{d'}"', "\shortmid"{marking}, no head, from=4-2, to=4-3]
	\arrow[""{name=4, anchor=center, inner sep=0}, "{\delrp_d}", from=3-2, to=4-2]
	\arrow["{\dnl_{d'}}"{description}, draw=none, from=0, to=2]
	\arrow["{(*)}"{description}, draw=none, from=4, to=3]
	\arrow["{\dnl_d}"{description}, draw=none, from=1, to=4]
\end{tikzcd}\]