Typesetting completed direct sum

Question

I'm trying to typeset a completed direct sum. This is traditionally written as a \bigoplus with a hat (really, a \widehat) above it. What is the recommended way to do this?

I can think of two solutions, but neither is optimal.

• \widehat{\bigoplus_i} V_i has too little spacing between the summation symbol and the argument.
• {\widehat\bigoplus}_i V_i has the index to the right of the summation symbol instead of beneath it, and it doesn't appear possible to fix this using \limits.

Answer 1

The trick is to use \mathop{\widehat{\bigoplus}}. Here I also adorn the construction to be the same as the other big operators in amsmath.

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\newcommand{\cbigoplus}{\DOTSB\cbigoplus@\slimits@}
\newcommand{\cbigoplus@}{\mathop{\widehat{\bigoplus}}}
\makeatother
\begin{document}
[
\bigoplus_{i\in I}V_i \hookrightarrow \cbigoplus_{i\in I}V_i
]
[
\cbigoplus_{i\in I}V_i \hookleftarrow \bigoplus_{i\in I}V_i
]
\begin{center} % just to make a smaller picture
$\bigoplus_{i\in I}V_i \hookrightarrow \cbigoplus_{i\in I}V_i$ \
$\cbigoplus_{i\in I}V_i \hookleftarrow \bigoplus_{i\in I}V_i$ 
\end{center}
\end{document}