library that can show a dropdown box with a list of choices to make when a cursor is blinking inside a text area of html

 Yes, there are several libraries that can provide this functionality. Some popular ones are:

1. jQuery UI Autocomplete - a plugin for the jQuery UI library
2. Select2 - a highly customizable select box replacement library
3. Typeahead.js - a fast and fully-featured autocomplete library
4. Autocomplete.js - a simple and lightweight autocomplete library

All of these libraries can be easily integrated into your HTML text area to provide a dropdown list of choices when the cursor is blinking.