Query
public void Linq84()
{
    List products = GetProductList();
  
    var categories =
        from p in products
        group p by p.Category into g
        let minPrice = g.Min(p => p.UnitPrice)
        select new { Category = g.Key, CheapestProducts = g.Where(p => p.UnitPrice == minPrice) };
  
    ObjectDumper.Write(categories, 1);
}
Lambda Expression
public void Linq84()
{
    List products = GetProductList();
 
    var categories = products.GroupBy(prod => prod.Category).
        Select(prodGroup => new {prodGroup, minPrice = prodGroup.Min(p => p.UnitPrice)}).
        Select(@t => new {
            Category = @t.prodGroup.Key,
            CheapestProducts = @t.prodGroup.Where(p => p.UnitPrice == @t.minPrice)});
 
    ObjectDumper.Write(categories, 1);
}
Output
Category=Beverages      CheapestProducts=...
  CheapestProducts: ProductID=24  ProductName=Guaraná Fantástica  Category=Beverages      UnitPrice=4.5000        UnitsInStock=20
Category=Condiments    CheapestProducts=...
  CheapestProducts: ProductID=3  ProductName=Aniseed Syrup      Category=Condiments    UnitPrice=10.0000      UnitsInStock=13
Category=Produce        CheapestProducts=...
  CheapestProducts: ProductID=74  ProductName=Longlife Tofu      Category=Produce        UnitPrice=10.0000      UnitsInStock=4
Category=Meat/Poultry  CheapestProducts=...
  CheapestProducts: ProductID=54  ProductName=Tourtière  Category=Meat/Poultry  UnitPrice=7.4500        UnitsInStock=21
Category=Seafood        CheapestProducts=...
  CheapestProducts: ProductID=13  ProductName=Konbu      Category=Seafood        UnitPrice=6.0000        UnitsInStock=24
Category=Dairy Products        CheapestProducts=...
  CheapestProducts: ProductID=33  ProductName=Geitost    Category=Dairy Products        UnitPrice=2.5000        UnitsInStock=112
Category=Confections    CheapestProducts=...
  CheapestProducts: ProductID=19  ProductName=Teatime Chocolate Biscuits  Category=Confections    UnitPrice=9.2000        UnitsInStock=25
Category=Grains/Cereals        CheapestProducts=...
  CheapestProducts: ProductID=52  ProductName=Filo Mix    Category=Grains/Cereals        UnitPrice=7.0000        UnitsInStock=38