I want to do something like this:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
Hom_{K\cap {}_a^bK}
\end{align*}
\end{document}
But there seems that the _a^b is on the \cap and not attached to the K.
How might I do this right?

\prescriptcommand from themathtoolspackage gives incorrect alignment; Superscripts before a letter in math – Werner Jun 13 '13 at 14:00