atillaordog

The search fields simply filter the lists in their current box.
Use the settings page to manage the location of search fields.
Simple as the sun, using easy JS.
Especially useful when there are a lot of categories, like in case of a shop.
It needs jQuery to run ! 
Trims beginning and ending spaces ! 
Works with the classic editor of WordPress 5, the new editor has this functionality included.

WP Admin Category Search

The plugin works flawlessly and is very simple.

Works fine and solved my problem

This plugin adds search functionality to category-like taxonomies and dropdowns like author on add / edit post / page admin pages.

Themeisle

Valerio Souza

This plugin will completely remove the ‘/category/’ from your permalinks ( e.g. <code>mydomain.com/category/my-category/</code> to <code>mydomain.com/my-category/</code> ).
No configuration is required
<h4>Features</h4>
<ol>
<li>Better and logical permalinks like <code>mydomain.com/my-category/</code> and <code>mydomain.com/my-category/my-post/</code>.</li>
<li>Simple plugin – No configuration is required.</li>
<li>No need to modify wordpress files.</li>
<li>Doesn’t require other plugins to work.</li>
<li>Compatible with sitemap plugins.</li>
<li>Compatible with WPML.</li>
<li>Works with multiple sub-categories.</li>
<li>Works with WordPress Multisite.</li>
<li>Redirects old category permalinks to the new ones (301 redirect, good for SEO).</li>
</ol>
<h4>Heads up:</h4>
Read the <a href="https://wordpress.org/plugins/remove-category-url/faq/" rel="ugc">FAQ</a> before use.
Want to help? Use the <a href="https://wordpress.org/support/plugin/remove-category-url" rel="ugc">support</a>

Remove Category URL

This plugin removes '/category' from your category permalinks. (e.g. /category/my-category/ to /my-category/)

WP Admin Category Search vs Remove Category URL