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This should give you all child categories (if any) for paritcular assign category for the page.
Category c = Category.Find(CurrentPage.Category.First());
CategoryCollection allChildCategories = c.Categories;
What you do with CategoryCollection and how you move that to ViewModel is up to you - either you access this from view itself, add it to viewmodel as collection of categories or map to some more abstract-not-related-to-EPiServer-collection and then process and render that on the view. It depends on your overall MVC app structure and approach.
I'm building a website that will have a FAQ section.
On the FAQ page i'ld like to list all subcategories to Category named "FAQ". Clicking on a tag will then filter the faq items with ajax (I'll figure out this later)
How do I get a list av subcategories and write out them in a view in EPiServer 7 MVC Razor?
Thanks in advance.