Prev/next in same category

I’m trying to get my prev/next in category links to match the style of the theme, which uses this:

if ( ! function_exists( 'first_post_nav' ) ) :
/**
 * Display navigation to next/previous post when applicable.
 */
function first_post_nav() {
	// Don't print empty markup if there's nowhere to navigate.
	$previous = ( is_attachment() ) ? get_post( get_post()->post_parent ) : get_adjacent_post( false, '', true );
	$next     = get_adjacent_post( false, '', false );

	if ( ! $next && ! $previous ) {
		return;
	}
	?>
	<nav class="navigation post-navigation" role="navigation">
		<h1 class="screen-reader-text"><?php _e( 'Post navigation', 'first' ); ?></h1>
		<div class="nav-links">
			<?php
				previous_post_link( '<div class="nav-previous"><div class="post-nav-title">' . __( 'Previous post', 'first' ) . '</div>%link</div>', _x( '%title', 'Previous post link', 'first' ) );
				next_post_link(     '<div class="nav-next"><div class="post-nav-title">' . __( 'Next post', 'first' ) . '</div>%link</div>', _x( '%title', 'Next post link', 'first' ) );
			?>
		</div><!-- .nav-links -->
	</nav><!-- .navigation -->
	<?php
}
endif;

Is that code editable to display prev/next in cat rather than just prev/next links?