Classical grid layouts can result in very long pages on mobile devices. This can be a big usability problem, especially when you want to show more than one category to your visitors.
Switching the grid to a horizontal scrolling element on touch devices can simplify your mobile layout a lot here and the good news is: People are already very used to it, since it has been used on their favorite SNS apps and on many big websites for quite a while now.
I would recommend to combine horizontal scroll elements with a "see all" or "more" link aligned with the category headline.
Better do not add buttons underneath the horizontal scroll element, because it makes the layout look unorganized and for that harder to scan.