How do you put multiple things under a limit?

Question

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:

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.

Answer 1

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).

Answer 2

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{\lim_{\longleftarrow}}_{H\in\mathcal{F}}G/H

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
  \lim_{\stackrel{\longleftarrow}{H\in\mathcal{F}}}G/H

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

Answer 3

You could use \substack of amsmath:

\lim_{\substack{\longleftarrow\\H\in\mathscr{F}}}

Answer 4

\documentclass{article}
\usepackage{mathtools}
\begin{document}

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

\end{document}

Answer 5

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

\documentclass{article}

\usepackage{mathtools}

\DeclareMathOperator*{\ulalim}{\underleftarrow\lim}

\begin{document}

\[\ulalim_{i}G/H_{i}\approx\smashoperator{\ulalim_{H\in\mathcal{F}}}G/H\]

\end{document}

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.