You are using the get_the_terms() but this function is used to get the custom taxonomies.

Use the function get_the_category(); inside the WordPress loop and pass the get_the_ID() function which will get the current post ID in the loop.

get_the_category(get_the_ID());

                <?php
                  $args = array(
                    'post_type' => 'work',
                    'posts_per_page' => '9'
                  );
                  $work_loop = new WP_Query( $args );
                  if ( $work_loop->have_posts() ) :
                    while ( $work_loop->have_posts() ) : $work_loop->the_post();
                      // Set variables
                        $cat_ids                = get_the_ID();
                        $cat_names_array        = get_the_category($ids);
                        $work_category           = get_the_category( get_the_ID() );
                        $work_title             = get_field( 'work_title' );
                        $work_main_image        = get_field( 'work_main_image' );
                        $work_link              = get_field( 'work_title' );
                        $work_about             = get_field( 'work_about' );
                        // $work_category = get_the_terms( the_post()->ID, 'taxonomy' );
                      // Output
                      ?>
                      <a href="<?php echo $work_main_image['url']; ?>" class="single_item link <?php foreach ( $work_category as $key => $value) { echo $value->category_nicename . " "; } ?> col-md-4 col-sm-6 wow fadeInUp" data-wow-delay="0.3s">
                        <img src="<?php echo $work_main_image['url']; ?>" alt=""> 
                    </a>
                    <?php
                      endwhile;
                    wp_reset_postdata();
                  endif; 
                ?>

Cheers :)

You need to get the category object and then use a foreach loop to build your list.

This should work for you:

<?php $categories = get_categories(); ?>
<nav>
  <?php foreach ($categories as $category):?>
    <a href="<?php echo get_category_link($category->term_id); ?>" class="nav-link" id="<?php echo $category->name;?>"><?php echo $category->name;?></a>
  <?php endforeach; ?>
</nav>

get_* functions are return functions. They don't actually print anything. Given your code example, all you should need is an echo statement:

<?php 
global $post;
$category = reset(get_the_category($post->ID));
$category_id = $category->cat_ID;
?>

<a class="button" href="<?php echo get_category_link( $category_id ); ?>">&larr; Back to Portfolio</a>

ALTERNATIVE: The best way of doing this would be to keep everything in your loop for reuse in single or archive views, combined with the use of wp_get_post_categories. This is untested, but it should get you started with a general-use method of listing categories associated with a given post or set of posts:

<?php
if(have_posts()) : while(have_posts()) : the_post();
    $cats = wp_get_post_categories($post->ID);
    if($cats) : foreach($cats as $cat) : $category = get_category($cat);
    ?>
    <a class="button" href="<?php echo get_category_link($category->cat_ID); ?>">&larr; <?php echo $category->name ?></a>
    <?php
    endforeach;endif;
endwhile;endif;
?>

On a category page, you can use the function single_cat_title(), or the more generic single_term_title(). These functions pull from the global $wp_query object, via get_queried_object().

You can use get_queried_object(), which will return category object.

See documentation:

https://codex.wordpress.org/Function_Reference/get_queried_object

Pass the category id into get_category_link():

<?php
$category = get_the_category();
$link = get_category_link( $category[0]->term_id );
?>

Update Outputting in template:

<?php
$category = get_the_category();
$first_category = $category[0];
echo sprintf( '<a href="%s">%s</a>', get_category_link( $first_category ), $first_category->name );
?>

I will show you how to display a list of categories in WordPress and also mark the active category, see code below:

<?php
// Get the current queried object
$term    = get_queried_object();
$term_id = ( isset( $term->term_id ) ) ? (int) $term->term_id : 0;

$categories = get_categories( array(
    'taxonomy'   => 'category', // Taxonomy to retrieve terms for. We want 'category'. Note that this parameter is default to 'category', so you can omit it
    'orderby'    => 'name',
    'parent'     => 0,
    'hide_empty' => 0, // change to 1 to hide categores not having a single post
) );
?>

<ul>
    <?php
    foreach ( $categories as $category ) 
    {
        $cat_ID        = (int) $category->term_id;
        $category_name = $category->name;

        // When viewing a particular category, give it an [active] class
        $cat_class = ( $cat_ID == $term_id ) ? 'active' : 'not-active';

        // I don't like showing the [uncategoirzed] category
        if ( strtolower( $category_name ) != 'uncategorized' )
        {
            printf( '%3$s',
                esc_attr( $cat_class ),
                esc_url( get_category_link( $category->term_id ) ),
                esc_html( $category->name )
            );
        }
    }
    ?>
</ul>

Notes about the code above:

get_queried_object() retrieve the currently-queried object. For example:

• if you're on a single post, it will return the post object
• if you're on a page, it will return the page object
• if you're on an archive page, it will return the post type object
• if you're on a category archive, it will return the category object
• if you're on an author archive, it will return the author object
• etc.

But there are some implications when using get_queried_object(), you should not expect it to return a post type object even when is_post_type_archive() is true. Check it out for more info.

Also, note that get_queried_object() is a wrapper for $wp_query->get_queried_object(), so it returns a WP object data type.

get_categories()

get_categories() retrieve list of category objects. Currently accepts only one parameter - $args. The $args parameter specifies a list of arguments that should be used to retrieve categories. See get_terms() for additional options.

However, to get the category for a particular posts here's a simple function I wrote: How to get list of categories for a post

Sounds like you may want get_category_link - something like:

$categories = get_categories();
foreach ($categories as $cat) {
    $category_link = get_category_link($cat->cat_ID);
    echo '<a href="' . esc_url($category_link) . '" title="' . esc_attr($cat->name) . '">' . esc_html($cat->name) . '</a>';
}

should print out the links to the categories for you.

There is a function called get_category_link() which might be helpful for you. This will be able to generate an appropriate link without having to hard-code it, except for the category name or ID.

Examples from the Wordpress Codex:

<?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>

http://codex.wordpress.org/Function_Reference/get_category_link

Use:

get_category_link( $category_id );

See:

https://codex.wordpress.org/Function_Reference/get_category_link

In your specific case:

<?php
global $post;
$categories = get_the_category();

    foreach ($categories as $category) :

       $exclude = get_the_ID();
       $posts = get_posts('posts_per_page=4&category='. $category->term_id);

        foreach($posts as $post) :
         if( $exclude != get_the_ID() ) { ?>

                <a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>" class="post c-1"> Link to actual post</a>

    <?php } endforeach; ?>

<a href="<?php echo esc_url( get_category_link( $category->term_id ) ); ?>" title="View all" class="btn border"><i class="i-right-double-arrow"></i> View all <?php echo $category->name; ?></a>
<?php  endforeach; wp_reset_postdata(); ?>

you can use get_queried_object()

$category = get_queried_object();
echo $category->term_id;