\varprojlím and \varinjlím

Question

I am typing some texts in Spanish, and I need to use the symbols for inverse and direct limits—\varprojlim and \varinjlim respectively. The problem is that these symbols look like "lim" with an arrow below, but I need "lím" with an accent over i. Is there an easy way to define something like that?

I think I found the definitions in the amsmath sources:

\def\varinjlim{%
  \mathop{\mathpalette\varlim@{\rightarrowfill@\textstyle}}\nmlimits@
}
\def\varprojlim{%
  \mathop{\mathpalette\varlim@{\leftarrowfill@\textstyle}}\nmlimits@
}

But I am not sure how to modify this properly.

Thank you for your help.

Answer 1

You can solve it with a simple patch, which probably should be the default also for amsmath: Since babel-spanish already solves the problem for \lim, we can just use the command instead of the explicit lim in the definition of \varlim@.

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[spanish]{babel}

\usepackage{amsmath}
\usepackage{etoolbox}

\makeatletter
\patchcmd{\varlim@}{lim}{\lim}{}{}
\makeatother

\begin{document}

$\displaystyle\lim\varinjlim\varprojlim$

\end{document}

This is the output after adding \usepackage[sc]{mathpazo}:

For “colimit”:

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[spanish]{babel}
\usepackage[sc]{mathpazo}

\usepackage{amsmath}
\usepackage{etoolbox}

\DeclareMathOperator*{\colim}{co{\lim}}
\makeatletter
\patchcmd{\varlim@}{lim}{\lim}{}{}
\makeatother


\begin{document}

$\lim\colim\varinjlim\varprojlim$

\end{document}

Answer 2

You have to re-define \varlim@:

\documentclass[ a4paper, leqno]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amssymb, amsfonts, mathtools}

\makeatletter\def\varlim@#1#2{%
\vtop{\m@th\ialign{##\cr
\hfil$#1\operator@font l\'{i}m$\hfil\cr
\noalign{\nointerlineskip\kern1.5\ex@}#2\cr
\noalign{\nointerlineskip\kern-\ex@}\cr}}%
}
\makeatother

\begin{document}

\[ \varinjlim( E_{α},f_{α\,β}),\quad\varprojlim( E_{α},f_{β\,α}),\]%

\end{document}​