\underbrace{\begin{pmatrix} S_1 \\ S_2 \\ \vdots \\ S_s \end{pmatrix}}_{\in \; \mathfrak{M}_{s,1}(\mathbb R)}
\begin{xy} \xymatrix { U \ar@/_/[ddr]_y \ar@{.>}[dr]|{\langle x,y \rangle} \ar@/^/[drr]^x \\ & X \times_Z Y \ar[d]^q \ar[r]_p & X \ar[d]_f \\ & Y \ar[r]^g & Z } \end{xy}
\begin{xy} \xymatrix{ A \ar@(l,u)^{1_A}[] \ar_{g \, \circ \, f}[dr] \ar^f[r] & B \ar@(u,r)^{1_B}[] \ar^g[d]\\ &C \ar@(d,r)_{1_C}[] } \end{xy} \qquad \overset{F}{\xrightarrow[\qquad \text{Functor} \qquad]{}} \quad \begin{xy} \xymatrix{ A \ar@(l,u)^{1_{F(A)}}[] \ar_{F(g \, \circ \, g) \,=\, F(g) \, \circ \, F(g)}[dr] \ar^{F \, f}[r] & B \ar@(u,r)^{1_{F(B)}}[] \ar^{F \, g}[d]\\ &C \ar@(d,r)_{1_{F(C)}}[] } \end{xy}