You need to throw ToList()in the end or change the type of the result to IEnumerable<SomeObject>, because, as the error says, you cannot assign IEnumerable<T>a type to a variable List<T>.
someobjectsfiltered = someobjects.SelectMany(s => s.AnotherList.FindAll(a => a.category == SomeCategory))
.ToList();
Edit based on comments
If you want, this SomeObjectsone that has a list containing an item that matches the category that you can do with.
someobjectsfiltered = someobjects.Where( s => s.AnotherList.Any( a => a.category == SomeCategory ))
.ToList();
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