How to make a dotted arrow in a commutative diagram?

Here you are:

documentclass{article}
usepackage{tikz-cd}

 begin{document}

begin{tikzcd}[sep=huge]
A times X arrow[dotted]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
& Y
end{tikzcd}

end{document} 

Edit:

To be complete, here is a solution with pstricks which gives an easy control of the size of the dotted arrow. Load pst-node and use the psmatrix environnment:

$ psset{arrowinset=0.15, arrows=->, linejoin=1, nodesep=3pt, labelsep=1pt}
begin{psmatrix}[colsep=2cm]
  Atimes X & Ftimes X 
 & Y %
 ncline[linewidth=1.2pt, linestyle=dotted, dotsep=2pt]{1,1}{1,2}naput{bar{q}times 1_X}%
ncline{1,1}{2,2}nbput{q}
ncline{1,2}{2,2}naput{epsilon}
  end{psmatrix} $

As I said in my comments (and as has been copied by another user in the mean time) you can add keys like dotted. For a thicker and truly dotted line you can use this post, the normal "dots" are just small rectangles. You can also keep the arrow heads small when making the line thicker.

documentclass{article}
usepackage{tikz-cd}
begin{document}
begin{tikzcd}[sep=huge]  
A times X arrow[dotted]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
 & Y
end{tikzcd}
qquad
begin{tikzcd}[sep=huge]  
A times X arrow[dash pattern=on 0pt off 3.2pt,line cap=round,line width=0.8pt]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
 & Y
end{tikzcd}

bigskip
tikzset{thick true dots/.style={dash pattern=on 0pt off pi*#1,
line cap=round,line width=#1},
thick true dots/.default=0.8pt,
oricm/.style={-{cm to[width=1.5ex,length=0.8ex,line width=0.4pt]}}}
begin{tikzcd}[sep=huge]  
A times X arrow[thick true dots]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
 & Y
end{tikzcd}
qquad
begin{tikzcd}[sep=huge]  
A times X arrow[thick true dots=2pt]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
 & Y
end{tikzcd}

bigskip
begin{tikzcd}[sep=huge]  
A times X arrow[oricm,thick true dots]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
 & Y
end{tikzcd}
qquad
begin{tikzcd}[sep=huge]  
A times X arrow[oricm,thick true dots=2pt]{r}{bar{q}times 1_x} arrow[swap]{dr}{q} & F times X arrow{d}{epsilon} 
 & Y
end{tikzcd}
end{document}