\newcommand{\canlim}[1]{\big((#1\backslash i)\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[dd]_{Fg} \ar@{<-}@[steelblue][dr]^{Fϕ_1} \ar@[steelblue][rrrr]^-{α_{ia_1}}& && &G(ia_1)\ar[dd]^{Gg} \ar@{<-}@[crimson][ld]_{Gϕ_1} \\ & c \cong \lim\canlim{c} && &F(c) \ar@[crimson]@{-->}[rr]^-{∃!\;α_c} && \;G(c) \cong \lim G\canlim{c}\\ i(a_2) \ar@{<-}[ur]_{ϕ_2}& && F(ia_2) \ar@{<-}[ur]_{Fϕ_2} \ar[rrrr]_-{α_{ia_2}}& && &G(ia_2) \ar@{<-}[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@[mediumseagreen]@{<-}[dr]^{Fϕ_1'} \ar@[mediumseagreen][rrrr]^-{α_{ia_1'}}& && &G(ia_1') \ar@{<-}[ld]_{Gϕ_1'} \\ &c'\cong\lim\canlim{c'}\ar[uuuu]_f && &F(c')\ar@[crimson][uuuu]^{Ff} \ar@[crimson]@{-->}[rr]^-{\color{mediumseagreen} ∃!\;α_{c'}} \ar@[khaki]@{-->}[rruuuu]^-{\color{crimson}∃!} && G(c')\cong\lim G\canlim{c'} \ar@[crimson][uuuu]_{Gf} \\ i(a_2')\ar@{<-}[ur]_{ϕ_2'} \ar[uu]_{g'}& && F(ia_2')\ar@[mediumseagreen]@{<-}[ur]_{Fϕ_2'} \ar@[steelblue][uu]^{Fg'} \ar@[mediumseagreen][rrrr]_-{α_{ia_2'}}& && &G(ia_2')\ar@{<-}[lu]^{Gϕ_2'} \ar@[mediumseagreen][uu]_{Gg'}\\ }