Compositon and Repository pattern

fixed the issue. Will look into that further Your interface should describe all the methods you wish to be exposed. Your interfaces describe what a given class will implement, not how its implemented, thus not exposing the state of the class. This is good as it allows you to have several classes inherit from this interface and implement the same methods in different ways.
In your case, you want the ability to "Add" from your CategoryRepository. Luckily for you, you already have an interface for this, IBloggingRepository.

// Implementation of the repository
// Does not expose Add to the ICategoryRepository !!!
public class CategoryRepository : ICategoryRepository, IBloggingRepository
{
    private readonly DataContext _context;

    private readonly IBloggingRepository _bloggingRepo;

    public CategoryRepository(DataContext context, IBloggingRepository bloggingRepository) 
    {
        _context = context;
        _bloggingRepo = bloggingRepository;
    }
    // The implementation of the Add method
    public void Add<T>(T entity) where T : class
    {
        _bloggingRepo.Add(entity);
    }
}

// Exposes the IBloggingRepository methods to ICategoryRepository
public interface ICategoryRepository : IBloggingRepository
{
}

// Implementation of the repository
public class CategoryRepository : ICategoryRepository
{
    private readonly DataContext _context;

    private readonly IBloggingRepository _bloggingRepo;

    public CategoryRepository(DataContext context, IBloggingRepository bloggingRepository) 
    {
        _context = context;
        _bloggingRepo = bloggingRepository;
    }
    // The implementation of the Add method
    public void Add<T>(T entity) where T : class
    {
        _bloggingRepo.Add(entity);
    }
}

// Some model to be added to the repository
// Just for demonstration purposes
public class Blog
{
    public Blog() { }
}


public class CategoryController : Controller
{
    private readonly ICategoryRepository _categoryRepo;

    public CategoryController(ICategoryRepository categoryRepo)
    {
        _categoryRepo = categoryRepo;
    }

    public async Task<IActionResult> SaveCategory()
    {
       // _categoryRepo.bloggingRepo.Add();
       return await Task.Run(() => 
       {
           Blog blog = new Blog();
           _categoryRepo.Add(blog);
           // return IActionResult;

       }).ConfigureAwait(false);
    }
}