In the product listings of each category of the Prestashop admin 
is shown a miniature image of the product that facilitates its 
identification instantly. This way you avoid having to select the 
product one by one to know exactly what it is in case you have the 
same name. Why can not the same thing happen here? I do not know 
if someone has ever raised it but here is the solution.

By reflex-ocasion May 2017


Edit catalog/admin/categories.php
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Search:

  require('includes/application_top.php');


ADD below:

  define(CATEGORIES_IMAGE_HEIGHT, 35);
  define(CATEGORIES_IMAGE_WIDTH, 35);


NOTE: This forces you to display the square images.
      If it is not your case because you have them elongated 
      horizontally, vertically or in both cases at the same time, 
      comment on one of the two lines so that they do not deform.

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Search for standar version:

                <td class="dataTableContent"><?php echo '<a href="' . tep_href_link(FILENAME_CATEGORIES, 'cPath=' . $cPath . '&pID=' . $products['products_id'] . '&action=new_product_preview') . '">' . tep_image(DIR_WS_ICONS . 'preview.gif', ICON_PREVIEW) . '</a>&nbsp;' . $products['products_name']; ?></td>


Replace with:

                <td class="dataTableContent"><?php echo '<a href="' . tep_href_link(FILENAME_CATEGORIES, 'cPath=' . $cPath . '&pID=' . $products['products_id'] . '&action=new_product_preview') . '">' . tep_info_image($products['products_image'], $products['products_name'], CATEGORIES_IMAGE_WIDTH, CATEGORIES_IMAGE_HEIGHT) . '</a>&nbsp;' . $products['products_name']; ?></td>

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Search for BS EDGE version:

                <td class="dataTableContent"><?php echo '<a href="' . tep_href_link('categories.php', 'cPath=' . $cPath . '&pID=' . $products['products_id'] . '&action=new_product_preview') . '">' . tep_image('images/icons/preview.gif', ICON_PREVIEW) . '</a>&nbsp;' . $products['products_name']; ?></td>


Replace with:

                <td class="dataTableContent"><?php echo '<a href="' . tep_href_link('categories.php', 'cPath=' . $cPath . '&pID=' . $products['products_id'] . '&action=new_product_preview') . '">' . tep_info_image($products['products_image'], $products['products_name'], CATEGORIES_IMAGE_WIDTH, CATEGORIES_IMAGE_HEIGHT) . '</a>&nbsp;' . $products['products_name']; ?></td>

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That is all!