There's different ways to replace the front page image in Minimum Pro with a slider, one of which you'll find here. In this tutorial,
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Replace Home Section 1 Background Image With Slider in Parallax Pro
This tutorial provides the code which enables you to replace the home section 1 background image in the Parallax Pro child theme by
Add Soliloquy Background Slider Using Backstretch In Centric Pro
The code in this tutorial enables you to use Backstretch to display the Soliloquy slider behind the 1st widget and header in Centric Pro
Add Image Slider To Centric Pro Home Widget 1 Background
The code addition and modification in this tutorial enables you to replace the background to the home widget 1 with a slider like this
Minimum Pro – Replace Front Page After Header Image with Slide Show
This tutorial enables you to replace the after header image on the front page of the Minimum Pro child theme with a slider. Note : If
Add Slider To Front Page of Atmosphere Pro
This tutorial provides the code you can use to add a slider to the front page of the Atmosphere Pro child theme by StudioPress. The code