If you have deleted a category from your Category Manager, it hasn't actually been deleted entirely from your Joomla site. Joomla keeps these deleted categories just in case there are any published articles that are saved inside the category. You can actually restore and publish that category again, or you can delete it completely from your site. This article explains how to delete or publish a trashed category.
After logging into the back end of your site and going to the Category Manager, select "Trashed" from the "Select Status" drop down menu item. This will show a list of all the categories that you have trashed in the past. To publish these categories again, check the box next to the name of each category that you'd like to publish, and click on the "Publish" button in the toolbar.
The category or categories selected will be republished and will once again appear in the Category Manager as "Published" categories.
If you d like to delete any or all trashed Categories from the Category Manager entirely, first select "Trashed" from the Select Status drop down menu item to view the "Trashed Categories". Click on the box next to the name of each Category that you d like to delete completely, and click on the Empty trash button in the toolbar.
You will receive a blue message indicating that the category was successfully trashed. At this point, it is gone completely and cannot be restored unless you do an entire site restore from a previously created backup.
If you follow the steps above and receive a red message like the one below, there are still published articles that have been saved into this category, and you cannot delete the category.
If you'd like to delete this category, re-save the articles that are currently saved in that category into a new category. Once all articles are saved elsewhere, you will be able to delete the category.
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