Get all categories and posts in those categories

cat.php

      <?php
      
      //https://wordpress.stackexchange.com/questions/43426/get-all-categories-and-posts-in-those-categories
      
    $args = array( 
      'posts_per_page' => -1
  );

  $query = new WP_Query($args);   
  $q = array();

  while ( $query->have_posts() ) { 

      $query->the_post(); 

      $a = '<a href="'. get_permalink() .'">' . get_the_title() .'</a>';

      $categories = get_the_category();

      foreach ( $categories as $key=>$category ) {

          $b = '<a href="' . get_category_link( $category ) . '">' . $category->name . '</a>';    

      }

      $q[$b][] = $a; // Create an array with the category names and post titles
  }

  /* Restore original Post Data */
  wp_reset_postdata();

  foreach ($q as $key=>$values) {
      echo $key;

      echo '<ul>';
          foreach ($values as $value){
              echo '<li>' . $value . '</li>';
          }
      echo '</ul>';
  }