u := 1.0cm;

a := 0.3u;

pair corner[];
corner[1] := (-u,u);
for i=2 upto 4:
   corner[i] := corner[i-1] rotated 90;
endfor;

label(btex $A$ etex, corner[1]);
label(btex $X$ etex, corner[2]);
label(btex $X \cup_f Y$ etex, corner[3]);
label(btex $Y$ etex, corner[4]);

path p[];
p[1] := ((-u,u) shifted (a,0)) -- ((u,u) shifted (-a,0));
p[2] := p[1] rotatedabout((-u,u),-90);
p[3] := p[2] shifted (2u,0);
p[4] := ((-u,-u) shifted (a,0)) -- ((u,-u) shifted (-2.5a,0));

for i=1 upto 4:
   drawarrow p[i];
endfor;

def midof(expr p) =
   point length(p)/2 of p
enddef;

label.top(btex $i$ etex, midof(p[1]));
label.lft(btex $f$ etex, midof(p[2]));
label.rt(btex $\phi_Y$ etex, midof(p[3]));
label.bot(btex $\phi_X$ etex, midof(p[4]));