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<?php
$cat = get_the_category();
$catname = $cat[0]->cat_name; //カテゴリー名
$catslug = $cat[0]->slug; //スラッグ名
?>

//<span class=”スラッグ名”>でカテゴリー名を囲む

<span class="<?php echo $catslug; ?>"><?php echo $catname; ?></span>