I'm reading about inverse limits, and the notation sometimes requires some sort of index or set over which to take the inverse limit. It looks something like this:

enter image description here

How would I correctly TeX that? I tried something like {\lim_{\longleftarrow}}_{H\in\mathscr{F}} but the arrow and the set are side by side, not one over the other.

5 Answers 5


There is no need for \substack in this case: there are the \varinjlim and \varprojlim macros taking care of both direct and inverse limits, putting a subscript now results in the behaviour you're looking for (and everyone is mimicking using \substack).

  • Thanks Pieter, I didn't know such macros existed. Just was I was looking for.
    – yunone
    Commented Aug 19, 2011 at 19:19
  • @Pieter: You're right. Use \usepackage{mathtools} and then \underset{i}{\varinjlim} for inverse limit, and \underset{H\in\mathscr{F}}{\varprojlim} for direct limit (the latter requires \usepackage{mathrsfs} as well).
    – Werner
    Commented Aug 19, 2011 at 19:28
  • @Werner He needs \varprojlim when reproducing the examples, inverse limits are also known as projective limits. And why use \underset? Just \varprojlim_i will do fine, even in text style where it is appropriate for the limit to be on the right.
    – Pieter
    Commented Aug 19, 2011 at 19:33
  • @Pieter: You're right, again...
    – Werner
    Commented Aug 19, 2011 at 19:39

Without going into too much font detail, you can use the \mathop{<stuff>} command to make an operator of almost anything in mathmode. For example, here's a small modification to your initial try:

\mathop{\lim_{\longleftarrow}}_{i}G/H_i \approx

Mathop to define mathematical operators with limits

However, you may also be interested in stacking items on top of one another using \stackrel{<top>}{<bottom>}:

\lim_{\stackrel{\longleftarrow}{i}}G/H_i \approx

Stacking limits using \stackrel

Consider browsing through Herbert Voß' mathmode document. It is filled with typesetting information in mathmode.

  • @yunone: It does modify the fontsize slightly for the <upper> part. In this case \longleftarrow; that's why you see it being slightly shorter.
    – Werner
    Commented Aug 19, 2011 at 18:56

You could use \substack of amsmath:


substack example


\[ \lim_{\xleftarrow[i]{}}G/H_i \approx
   \lim_{\xleftarrow[\mathclap{H\in\mathcal{F}}]{}}G/H \]


enter image description here


You can define a new operator using \DeclareMathOperator of the amsmath package as follows:







The resulting output is:

Note the usage of \smashoperator to remove redundant white space between the operator and the operand on the right-hand side of the equation.

  • OK, in this specific case, you actually don't need to define a new operator since there is already one as pointed out by @Pieter.
    – mhp
    Commented Aug 19, 2011 at 20:09

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