\[\newcommand{\colim}{\mathop{\rm colim}\nolimits}
\newcommand{\cancol}[1]{\big((i/#1)\stackrel{\mathrm{pr}_𝔸}{→} 𝔸 \stackrel{i}{→} ℂ\big)}
\definecolor{purple}{RGB}{128,0,128}
\definecolor{orchid}{RGB}{218,112,214}
\definecolor{crimson}{RGB}{220,20,60}
\definecolor{salmon}{RGB}{250,128,114}
\definecolor{brown}{RGB}{165,42,42}
\definecolor{chocolate}{RGB}{210,105,30}
\definecolor{sandybrown}{RGB}{244,164,96}
\definecolor{darkorange}{RGB}{255,140,0}
\definecolor{khaki}{RGB}{240,230,140}
\definecolor{greenyellow}{RGB}{173,255,47}
\definecolor{lightseagreen}{RGB}{32,178,170}
\definecolor{mediumseagreen}{RGB}{60,179,113}
\definecolor{olivedrab}{RGB}{107,142,35}
\definecolor{teal}{RGB}{0,128,128}
\definecolor{cadetblue}{RGB}{95,198,160}
\definecolor{aquamarine}{RGB}{127,255,212}
\definecolor{steelblue}{RGB}{70,130,180}
\definecolor{navy}{RGB}{0,0,128}
\definecolor{midnightblue}{RGB}{25,25,112}
\xymatrix{
i(a_1) \ar[dd]_{g} \ar[dr]^{ϕ_1}& && F(ia_1) \ar@[mediumseagreen][dd]_{Fg} \ar[dr]^{Fϕ_1}
\ar@[mediumseagreen][rrrr]^-{α_{ia_1}}& && &G(ia_1)\ar@[steelblue][dd]^{Gg}
\ar@[mediumseagreen][ld]_{Gϕ_1} \\
& c \cong \colim\cancol{c} && &F(c) \cong \colim F\cancol{c}
\ar@[crimson]@{-->}[rr]^-{\color{mediumseagreen}∃!\;α_c} && \;G(c) \\
i(a_2) \ar[ur]_{ϕ_2}& && F(ia_2) \ar[ur]_{Fϕ_2}
\ar@[mediumseagreen][rrrr]_-{α_{ia_2}}& && &G(ia_2) \ar@[mediumseagreen][lu]^{Gϕ_2}\\
& \ar@{}[rr]^(.25){}="a"^(.75){}="b" \ar@{|.>}^{F \, , \;G} "a";"b" && \\
i(a_1') \ar[dr]^{ϕ_1'}& && F(ia_1') \ar@[crimson][dr]^{Fϕ_1'}
\ar@[steelblue][rrrr]^-{α_{ia_1'}}& && &G(ia_1') \ar@[steelblue][ld]_{Gϕ_1'} \\
&c'\cong\colim\cancol{c'}\ar[uuuu]_f && &F(c')\cong\colim F\cancol{c'}\ar@[crimson][uuuu]^{Ff}
\ar@[crimson]@{-->}[rr]^-{∃!\;α_{c'}}
\ar@[khaki]@{-->}[rruuuu]^-{\color {crimson}∃!} && G(c')\ar@[crimson][uuuu]_{Gf} \\
i(a_2')\ar[ur]_{ϕ_2'} \ar[uu]_{g'}& && F(ia_2')\ar[ur]_{Fϕ_2'}\ar[uu]^{Fg'}
\ar[rrrr]_-{α_{ia_2'}}& && &G(ia_2')\ar[lu]^{Gϕ_2'}\ar[uu]_{Gg'}\\
}\]
