bigsqcup with sideset doesn't shrink in subscript

Question

I'm using a \bigsqcup that involves a \sideset inside a subscript for a function, but the \bigsqcup symbol doesn't get smaller like everything else. Is there a way to make it shrink proportionally with the other symbols while using \sideset?

Here's a self contained example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}
  \begin{equation*}
    \bigsqcup_{\sideset{}{_B}\bigsqcup V} A
  \end{equation*}
\end{document}

It displays like this:

Answer 1

The point is that \sideset just isn't designed to be used in sub- and superscripts: it issues an explicit \displaystyle in which the big operator will be typeset. In your case, you can just use \bigsqcup_B V in the subscript, as Peter suggests in his comment. The B is set at the side since it's in a subscript. (In other cases, you can use \bigsqcup\nolimits_B V.)

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}
  \begin{equation*}
    \bigsqcup_{\bigsqcup_B V} A
  \end{equation*}
\end{document}