How to type sheaf hom

An ugly hack, but it looks pretty good:

\documentclass{article}
\usepackage{amsmath,calligra,mathrsfs}
\DeclareMathOperator{\Hom}{\mathscr{H}\text{\kern -3pt {\calligra\large om}}\,}

\begin{document}
$\Hom(X,Y)$
\end{document}

The result:

\newcommand*{\sheafhom}{\mathrm{H}\kern -.5pt om}