[math]\displaystyle{
\require{AMSmath}
\require{AMSsymbols}
\newcommand\mapright[2][]{\xrightarrow[#1]{ #2 }}
\newcommand\mapleft[2][]{\xleftarrow[#1]{ #2 }}
\newcommand\mapdown[2][]{\llap{\raise2pt{\scriptstyle{ #1 }}}\Big\downarrow\rlap{\raise2pt{\scriptstyle{ #2 }}}}
\newcommand\mapup[2][]{\llap{{\scriptstyle{ #1 }}}\Big\uparrow\rlap{{\scriptstyle{ #2 }}}}
\newcommand\mapdownright[2][]{\vcenter{\kern3pt\raise.5pt\rlap{\lower6pt{\scriptstyle#1}}\kern-2pt\diagdown\kern-.42em\lower.63em{\searrow}\raise-.5pt\kern-2pt\llap{\raise1.5pt{\scriptstyle#2}}}}
\newcommand\mapdownleft[2][]{\vcenter{\kern14pt\rlap{\lower6pt{\scriptstyle#1}}\kern-14pt\kern1em\diagup\kern-1.6em\lower.63em{\swarrow}\llap{\raise2pt{\scriptstyle #2\kern2pt}}}}
\begin{array}{ccc}
\mapright{a} & \mapright[b]{a} & \mapleft{a} & \mapleft[b]{a} \\[3pt] \mapdown{a} & \mapdown[b]{a} & \mapup{a} & \mapup[b]{a} \\[3pt] \mapdownright{a} & \mapdownright[b]{a} & \mapdownleft{a} & \mapdownleft[b]{a} \\[3pt]
\end{array} }[/math]