Test

Misc. macros: $\Newextarrow{\xLongrightarrow}{3,2}{0x21D2} \Newextarrow{\xrightrightarrows}{5,5}{0x21C9}$

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123, 1\mathop2 3, 1\mathop{2}3, 1{\mathop2}3, 1{\mathop{2}}3 $$123, 1\mathop2 3, 1\mathop{2}3, 1{\mathop2}3, 1{\mathop{2}}3$$

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${\bf Span}({\bf Graph})$ $S^{{\mathcal{W}}_\Lambda}\otimes T$
$$\begin{equation}\begin{CD} S^{{\mathcal{W}}_\Lambda}\otimes T @>j>> T\\ @VVV @VV{{\rm End}\, P}V\\ (S\otimes T)/I @= (Z\otimes T)/J \end{CD}\end{equation}$$ $$\begin{equation}\begin{CD} A @>a>> B\\ @VbVV @VVcV\\ C @>d>> D \end{CD}\end{equation}$$
A significant principal $S_n$-bundle ($n \in \bf\text{N}$, $X \in \bf\text{Set}$): $$\begin{equation}\begin{CD} S_{[n]} @>>> \homst {[n]} \Inj X\\ \text{ } @VV\text{image}V\\ \text{} @. \mathcal{P}^{[n]} (X)\\ \end{CD}\end{equation}$$ An important adjunction (in combinatorics and elsewhere; $X \in \bf\text{Set}$): $$\begin{equation}\text{\substack:}\qquad \mathrel{\mathcal{SPart}(X) \substack{\xrightarrow{X/-} \\\xleftarrow[\kernelpart]{}} X\downarrow\Surj} \end{equation}$$

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$$\binom {n} {k} \left\{ \begin{aligned} n\\ k \end{aligned} \right\}$$ \buildrel: $\buildrel \text{action associativity} \over =$ and \stackrel: $\stackrel {\text{action associativity}} =$ $$\text{\Newextarrow:}\qquad \Newextarrow{\xequals}{5,5}{0x003D} \xequals{\text{long message}}$$ $$\text{\Newextarrow:}\qquad \Newextarrow{\xequals}{5,5}{0x21C9} \xequals{\text{long message}}$$ $$\text{\xlongequal:}\qquad \xlongequal{\text{long message}}$$ $\Aut X \quad \homst X\Set Y _{subscript1}text_{subscript2}$ $$\text{\atop:}\qquad X {\longrightarrow \atop \longrightarrow} Y$$ $$\hbox{text 1} \qquad \raise10pt{\hbox{text 2}}$$ $\def\graphsoverx{\leftcat{\Set\mathord\downdownarrows}X} \def\setsunderx{X\rightcat{\mathord\downarrow\Set}}$ $\graphsoverx \quad \setsunderx$

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$$\begin{array}{} \Sub (\N) & \xrightarrow{\textstyle \text{least}} & \bftwo^\op \\ & \llap{{?}\notin{?}'} \searrow & \Bigg\Updownarrow \rlap{\mkern-57mu \text{least}{+}{+}PCON} & \searrow \rlap\neg \\ && [\N,\bftwo] & \xrightarrow[\textstyle PCON]{} & \bftwo \\ \end{array}$$