<xsl:param name="target_category" select="'3'"/>
<xsl:template match="//category[@b='3']">

The preceding line works, but what I really want is:

<xsl:template match="//category[@b={$target_category}]">

Parameter or variable referencces are not allowed in match patterns.
You can work around this restriction by using a conditional.
BTW the "//" starting the match pattern is almost always redundant.
 <xsl:template match="category">
   <xsl:if test="@b=$target_category">
     ...