Show name, image and link of wordpress categories - php

Question

I need to show some categories in my home page, and show the category image, and also the link of the same. Using the WORDPRESS.
For them to stick to the same style of example is not the problem. I'm having difficulties appearing, that is, the problem is in the code that calls the categories and their attributes like: image, link and title.
Example
Here's what I'm trying to do:
<section id=""
class="projects">
<div class="js-projects-gallery">
<div class="projects_block row">
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
<?php
$args = array(
'show_option_all' => '',
'echo' => 1,
'hide_empty' => 0,
'style' => 'list',
'title_li' => __('Categorias')
);
?>
<div class="project project_item col-sm-6 col-md-4 col-lg-3">
<?php foreach (get_categories($args) as $cat) : ?>
<a class="link" href="<?php echo get_category_link($cat->term_id); ?>"
title="<?php echo $cat->cat_name; ?>">
<figure>
<img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>"
class="size-goarch-image-480x880-croped">
<figcaption>
<h3 class="project-title">
<?php echo $cat->cat_name; ?>
</h3>
<h4 class="project-category">
<?php echo $cat->cat_name; ?>
</h4>
<div class="project-zoom"></div>
</figcaption>
</figure>
</a>
<?php endforeach; ?>
</div>
<?php endwhile; else: ?>
<div class="project project_item col-sm-6 col-md-4 col-lg-3">
<p><?php echo "Sorry, we have nothing posted yet."; ?></p>
</div>
<?php endif; ?>
</div>
</div>
</section>