How to use DI container to resolve dependencies in Strategy Pattern?

I currently working on an application that will act differently based on userInput. So I think about the Strategy Pattern. Below is my implementation:

I have some business logic:

interface IBusinessLogic
{
   void DoBusinessLogic();
}

class TypeABusinessLogic : IBusinessLogic
{
   public void DoBusinessLogic()
   {
      Console.WriteLine("Do Business Logic for Type A");
   }
 } 

class TypeBBusinessLogic : IBusinessLogic
{
   public void DoBusinessLogic()
   {
      Console.WriteLine("Do Business Logic for Type B");
   }
}  

And, also some application logic:

interface IApplicationLogic
{
   void DoApplicationLogic();
}

class TypeAApplicationLogic : IApplicationLogic
{
   public void DoApplicationLogic()
   {
      Console.WriteLine("Do Application Logic for Type A");
   }
 } 

class TypeBApplicationLogic : IApplicationLogic
{
   public void DoApplicationLogic()
   {
      Console.WriteLine("Do Application Logic for Type B");
   }
}    

Now, my strategies need to do both business logic and application logic

interface IStrategy
{
   void DoWork();
}

abstract class StrategyBase : IStrategy
{
   private IBusinessLogic _businessLogic;
   private IApplicationLogic _applicationLogic;

   protected StrategyBase(IBusinessLogic businessLogic, IApplicationLogic applicationLogic)
   {
      _businessLogic = businessLogic;
      _applicationLogic = applicationLogic;
   }

   public void DoWork()
   {
      _businessLogic.DoBusinessLogic();
      _applicationLogic.DoApplicationLogic();
   }
}

class TypeAStrategy : IStrategy
{
   public TypeAStrategy(TypeABussinessLogic businessLogic, TypeAApplicationLogic applicationLogic) : base(businessLogic, applicationLogic)
   {}
}

class TypeBStrategy : IStrategy
{
   public TypeBStrategy(TypeBBussinessLogic businessLogic, TypeBApplicationLogic applicationLogic) : base(businessLogic, applicationLogic)
   {}
}

Now is my Context class

class Context
{
   private Func<string, IStrategy> _strategyFactory;
   public Context(Func<string, IStrategy> strategyFactory)
   {
      _strategyFactory = strategyFactory;
   } 
   public void Run()
   {
      string userInput = GetUserInput(); //"TypeA" or "TypeB"
      IStrategy strategy = _strategyFactory(userInput);
      strategy.DoWork();
   }
}

The problem I can see here is my strategies (TypeAStrategy, TypeBStrategy) depend directly on concrete class (TypeABusinessLogic,TypeAApplicationLogic,TypeBBusinessLogic, TypeBApplicationLogic).

If I let my strategies depend on interfaces, I dont know how to implement DI container to resolve dependencies (Notes: I currently using Autofac, but I can use any other DI containers )

Please advise.