# Is there a “medium” \cap?

When displaying the intersection symbol in equations, e.g.,

$$Hom(A,B) \cap Hom(B,C)$$


I find that the "cap" is too small; its height is, in fact, subordinate to the surrounding content. On the other hand, \bigcap is entirely too big, dwarfing the surrounding content. This is especially unnecessary if the intersection is not indexed, for example. What is needed is a "medium" cap whose size is somewhere between the big cap and the regular cap. Does such a symbol/construct exist?

Note that similar comments apply to \bigcup and \cup.

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\ifx\displaystyle#1\textstyle\else#1\fi\bigcap\$}}}


This is the result of

$\operatorname{Hom}(A,B)\cap\operatorname{Hom}(B,C)$


and of

$\operatorname{Hom}(A,B)\mcap\operatorname{Hom}(B,C)$


You need \usepackage{amsmath} to use \operatorname and you might want to say

\DeclareMathOperator{\Hom}{Hom}


in the preamble, in order to be able to use \Hom as an abbreviation.

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You can use scalerel from the scalerel package to create one:

\documentclass{article}
\usepackage{scalerel}

\begin{document}
$Hom(A,B) \cap Hom(B,C)$
$Hom(A,B) \scalerel{\cap}{Hom(B,C)}$
$Hom(A,B) \mathbin{\scaleobj{1.75}{\cap}} Hom(B,C)$
$Hom(A,B) \mathbin{\scaleobj{0.9}{\bigcap}} Hom(B,C)$
$Hom(A,B) \bigcap Hom(B,C)$
\end{document}

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Probably \mathbin{\scalerel{\cap}}, if you want correct spacing. – egreg Jan 11 at 16:43
I am afraid not because \scalerel is a two arguments command. Said that, it is true that the spacing is not correct. – Spherical Triangle Jan 11 at 18:03
Instead we can use \scaleobj. I added the corresponding material. – Spherical Triangle Jan 12 at 5:01