Dynamically load posts based on category

No there is no such premade code to load posts based on which categories are selected without reload the page content. There are two option you can imply. 

Option 1: Using Ajax
Option 2: Loading all the content and hide/show using CSS & jQuery tricks

Note: Option 2 increase your initial load time as you need to fetch all the content from all the category and show some post initially with CSS tricks. And on click of the specific category you can then with help of jQuery & CSS you can manipulate the display.

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