There is no functionality built-in to Prestashop to enable you to set shipping costs based on a category rather than a product. If this is a requirement of yours, I would suggest:
Looking for and installing, or developing your own, custom module to give you this functionality. Your module for each category could let you set a shipping price and/or other parameters and then when you click save goes through all the products in that category and overwrites their existing shipping price details with those you have specified. I would start off by looking through the Prestashop Marketplace before browsing the web more generally.
Trying a desktop software package for managing your product catalogue and shipping details etc that suits your requirements, but that also integrates with Prestashop via the API and can therefore synchronise to update the product catalogue. I don't have a specific software in mind but am aware that products such as this exist.
Personally I prefer option 1 though this might take some work. I'm not aware of a third party module that does this. If you're not a skilled PHP developer you may need to contact a commercial module developer (for example, Presto Changeo) to ask them if they would consider developing a module to meet your requirements, that they could then add to their product portfolio and sell to other customers aswell.
Note: I have no personal or professional association with Presto Changeo whatsoever other than I have identified they might be a suitable third party commercial module developer and felt it helpful to signpost the asking party. Other great developers will exist if you search for them.