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.

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.

WP Admin Category Search vs Allow HTML in Category Descriptions