In the standard implementation of the SharePoint calendar app it is not possible to visualize the event entries with a different background color depending on the category. To implement such a feature we have to do some customizing.
In the following steps we will modify the calendar with an additional column that holds auto-calculated informations. After that we will implement a JavaScript code block that contains the coloring logic.

Some events with different categories in the standard calendar implementation.
Caution: The jQuery JavaScript library must be available in your environment.
Read More »SharePoint 2013: Calendar – Colorize Event Categories