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<?php
    // Get the ID of a given category
    $category_id = get_cat_ID( 'Category Name' );

    // Get the URL of this category
    $category_link = get_category_link( $category_id );
?>

<!-- Print a link to this category -->
<a href="<?php echo esc_url( $category_link ); ?>" title="Category Name">Category Name</a>