This plugin allows to set a featured image for each category. 
Posts without a featured image set will show the category’s featured image instead. 
Featured images usually are placed by the theme in the single post page, in the latest posts page, etc. 
But can also be shown using the shortcode [cfi_featured_image] or the PHP function cfi_featured_image(). To get the featured image URL I added the function cfi_featured_image_url().
Shortcode/PHP function optional arguments:
<ul>
<li>‘size’: ‘thumbnail’, ‘medium’, ‘large’, ‘full’</li>
<li>‘class’: class of the image tag</li>
<li>‘alt’: alternative text of the image tag</li>
<li>‘title’: title of the image tag</li>
<li>‘cat_id’: select a specific category id</li>
</ul>
Shortcode example:
<pre><code>[cfi_featured_image size="large" title="This is a test..." class="my-image" alt="My image"]
</code></pre>
Function example 1:
<pre><code>cfi_featured_image( array( 'size' => 'large', 'title' => 'This is a test...', 'class' => 'my-image', 'alt' => 'My image' ) );
</code></pre>
Function example 2:
<pre><code>cfi_featured_image_url( array( 'size' => 'large' ) );
</code></pre>
Notes:
<ul>
<li>If a post has more than a category with a featured image the first available is loaded</li>
<li>If a category hasn’t a featured image but it has a parent category with a featured image the parent one is loaded</li>
</ul>

Category Featured Images

This plugin does one thing and it does it well.
It's easy to use, too: install, set up the default category images and forget about it.



Does one thing and does it well

Set a featured image for all the posts of a category.

Arno Esterhuizen

When you add text to the category description textarea and save the category, WordPress runs content filters that strips out all but the most basic formatting tags.
This plugin disables those filters for roles with the necessary permissions. Any html code you add to the category description will not be stripped out.
This plugin does not do anything other than disable the filters. It does not protect you from entering invalid HTML, nor does it help you create WYSIWYG HTML. You can use the post or page composing screen to help you create the text and formatting. Switch to the ‘code’ tab and copy the HTML code into the category description field.

Allow HTML in Category Descriptions

Great Plugin

This plugin allows you to use unfiltered HTML in your category descriptions by disabling selected WordPress filters.

Category Featured Images vs Allow HTML in Category Descriptions