Otdfbt

I have a quite large description of an arrow, and row sep = huge does not make the arrow long enough. Is there a way to format this better?

documentclassarticle
usepackageamsmath
usepackageamssymb
usepackagetikz-cd
usepackagefullpage
usepackageamsthm
usepackageadjustbox
usepackagexcolor
begindocument
begintikzcd[column sep = huge, row sep = huge]
E arrow[r, "e"] & Pi_i in ob(mathcalE) F(i) arrow[r, shift left, " 
 u in hom(mathcalE)>"] arrow[r, shift right, " u in hom(mathcalE)"'] & Pi_u in hom(mathcalE) 
F(cod(u)) 
endtikzcd
enddocument

Here are two different ways

documentclassarticle

usepackageamsmath
usepackageamssymb
usepackagetikz-cd

DeclareMathOperatorcodcod
DeclareMathOperatordomdom
DeclareMathOperatorobob

begindocument

Option 1: wide column separation specified by dimension
beginequation*
 begintikzcd[column sep = 10em]
 E arrow[r, "e"] & displaystyleprod_i in
 ob(mathcalE) mkern-12mu F(i)
 arrow[r, shift left, " langlepi_cod(u) mid u in
 hom(mathcalE)rangle"] arrow[r, shift right, "langle F(u)
 pi_dom(u) mid u in
 hom(mathcalE)rangle"']
 & displaystyleprod_u in hom(mathcalE) mkern-12mu F(cod(u))
 endtikzcd
endequation*

Option 2: let arrows cover two (or more) columns
beginequation*
 begintikzcd[column sep = huge]
 E arrow[r, "e"]
 & displaystyleprod_i in ob(mathcalE) mkern-12mu F(i)
 arrow[rr, shift left, " langlepi_cod(u) mid u in
 hom(mathcalE)rangle"]
 arrow[rr, shift right, "langle F(u) pi_dom(u)
 mid u in hom(mathcalE)rangle"']
 && displaystyleprod_u in hom(mathcalE) mkern-12mu F(cod(u))
 endtikzcd
endequation*

enddocument

The first is simply to specify the column sep as a dimension.
The second is to add an extra column under the long arrows, so you have

A arrow[r] & B arrow[rr] && C

instead of

A arrow[r] & B arrow[r] & C

You can make this wider by using more columns

A arrow[r] & B arrow[rrr] &&& C

etc.

Note I have recoded much of your mathematics.

The above solutions corresponding to working with a fixed grid, which is often a good idea for consistent spacing. An alternative is the extra space syntax of egreg's answer:

&[5em]

in the first row, will push the subsequent column 5em to the right and so making the corresponding arrows longer.

Add a width specification:

documentclassarticle
usepackageamsmath
usepackageamssymb
usepackagetikz-cd

DeclareMathOperatorobob
DeclareMathOperatordomdom
DeclareMathOperatorcodcod

begindocument

begintikzcd
E arrow[r, "e"] &
 prod_i in ob(mathcalE) F(i)
 arrow[
 r, shift left,
 "langlepi_cod(u) mid u in hom(mathcalE)rangle"
 ]
 arrow[
 r, shift right,
 "langle F(u)pi_dom(u) mid u in hom(mathcalE)rangle"'
 ] &[8em]
 prod_u in hom(mathcalE) F(cod(u))
endtikzcd

enddocument

Note the adjustments I made:

• 
  <...> should be langle...rangle
  


• 
  Pi should be prod
  


• 
  | should be mid
  


• ob, dom and cod should be typeset upright

A possible alternative with smashoperator that makes the diagram shorter:

documentclassarticle
usepackageamsmath,mathtools
usepackageamssymb
usepackagetikz-cd

DeclareMathOperatorobob
DeclareMathOperatordomdom
DeclareMathOperatorcodcod

begindocument

begintikzcd
E arrow[r, "e"] &
 smashoperatorprod_i in ob(mathcalE) F(i)
 arrow[
 r, shift left,
 "langlepi_cod(u) mid u in hom(mathcalE)rangle"
 ]
 arrow[
 r, shift right,
 "langle F(u)pi_dom(u) mid u in hom(mathcalE)rangle"'
 ] &[10em]
 smashoperatorprod_u in hom(mathcalE) F(cod(u))
endtikzcd

enddocument

Add an empty column between columns 2 and 3. I also added some improvements to the diagram.

documentclassarticle
usepackageamsmath
usepackageamssymb
usepackagetikz-cd
usepackagefullpage
usepackageamsthm
usepackageadjustbox

begindocument

begintikzcd[column sep= huge, row sep=huge]
E arrow[r, "e"] & Pi_i in ob(mathcalE) F(i) arrow[rr, shift left=1ex, "
langlepi_cod(u) , "] arrow[rr, shift right=1ex, " , u in hom(mathcalE)rangle"'] & & Pi_u in hom(mathcalE)
F(cod(u))
endtikzcd

enddocument 

I remade everything in normal TikZ and correct (many) typos. Also, take note that I use langle and rangle instead of < and >. A curve is always more readable than a straight line in this case in my opinion.

documentclassstandalone
usepackageamsmath
usepackagetikz
usetikzlibrarypositioning
DeclareMathOperatorobob
DeclareMathOperatorcodcod
DeclareMathOperatordomdom
begindocument
begintikzpicture[>=stealth]
node (mid) $prod_i in ob(mathcalE) F(i)$;
node[left=1cm of mid] (left) $E$;
node[right=4cm of mid] (right) $prod_u in hom(mathcalE)F(cod(u))$;
draw[->] (left)--(mid) node[midway,above] $scriptstyle e$;
draw[->] ([yshift=.2em]mid.east) to[bend left=5] node[midway,above] $scriptstylelanglepi_cod(u) ([yshift=.2em]right.west);
draw[->] ([yshift=-.2em]mid.east) to[bend right=5] node[midway,below] $scriptstylelangle F(u)pi_dom(u) ([yshift=-.2em]right.west);
endtikzpicture
enddocument