Collection with Generic Index
The problem

There is a massive hole in your logic here. You are relying on the fact that there exists a property whose type is equal to the name of the property.

public MyEnumProperty MyEnumProperty { get; set; }


Your class would become unusable if I changed this line to:

public MyEnumProperty MyProperty { get; set; }


To explain the issue in detail, the rest of my answer will assume that you're using this second case where the type and name do not match.

The problem is here:

t =&gt; t.GetType()
      .GetProperty(index.GetType().Name)  // &lt;== HERE
      .GetValue(t)
      .Equals(index)


GetProperty retrieves a property based on its name (MyProperty). So, what name are you using?

index.GetType().Name


The name of the type (MyEnumProperty). Which is not the same as the MyProperty name that you're looking for.

Let's look at another implementation of your class, where we will use MyIntProperty as the index:

var myCollection = new IndexableCollection&lt;MyClass, int&gt;();

var element = myCollection[5];


Going by the intention of your code, this should be possible. After all, you have made no specific requirements for the given TIndex, which means that your class needs to work for all possible types.

But it doesn't, because when you try to access myCollection[5], you get:

t =&gt; t.GetType()
      .GetProperty("Int32")
      .GetValue(t)
      .Equals(index)


There is no property by the name of Int32, so it does not work.



The solution

In essence, you are trying to define the indexed property by its type alone, which is a dangerous thing to do.

We could rewrite the code to search MyClass for the first property of the given type TIndex. However, what will you do if MyClass has multiple properties of that same type? 

You'd be stuck guessing at the intended index, and that's not a good solution either.

What we're missing is the definition of the exact property you want to use as an index. You're trying to find it by its type alone, and that is not enough. Instead, you need a way to select the correct property.

My solution: the lambda.

You need a mapping between the element (TElement) and its intended index (TIndex). This is the perfect situation to use a lambda method of type Func&lt;TElement, TIndex&gt;.

I updated your code to a working example with lambdas. I slightly tweaked your code for the sake of example:

public enum MyEnum { One, Two, Three }

public class MyClass
{
    public int MyIntProperty { get; set; }
    public string MyStringProperty { get; set; }
    public MyEnum MyEnumProperty { get; set; }
}


The collection class:

public class MyCollection&lt;TElement, TIndex&gt; : List&lt;TElement&gt;
{
    private Func&lt;TElement, TIndex&gt; _indexMapping { get; set; }

    public MyCollection(Func&lt;TElement, TIndex&gt; indexMapping)
    {
        _indexMapping = indexMapping;
    }

    public TElement this[TIndex index]
    {
        get
        {
            return base.Find(t =&gt; _indexMapping.Invoke(t).Equals(index));
        }
    }
}


The only real difference is that we now store a Func&lt;TElement, TIndex&gt; _indexMapping. This gives us the mapping between the element and its index.
This has the interesting side effect that you can't use a TIndex that doesn't exist as a property in TElement (unless you supply a constant value unrelated to the element, but then you're being silly).

base.Find(t =&gt; _indexMapping.Invoke(t).Equals(index));


When iterating over the list, we simply invoke the mapping (on the element t), which returns the value of its intended index. All we have to do then is check whether the value matches the index that was currently given as a parameter, which is easily done by calling .Equals().

Example usages:

//Enum as index

var myCollection = new MyCollection&lt;MyClass, MyEnum&gt;(o =&gt; o.MyEnumProperty);
var element = myCollection[MyEnum.One];

//Int as index

var myCollection = new MyCollection&lt;MyClass, int&gt;(o =&gt; o.MyIntProperty);
var element = myCollection[12345];

//String as index

var myCollection = new MyCollection&lt;MyClass, String&gt;(o =&gt; o.MyStringProperty);
var element = myCollection["Hello"];




Tangential comments


If your index is a custom class, make sure to implement the correct equality comparison! The default behavior (checking if it's the same object in memory) may or may not be what you want.
There's still an issue when your collection contains multiple items with the same index. You'll always receive the first matching item, the others will essentially be invisible (until you remove the first item). Again, depending on your requirements, that might be intentional behavior, or it might not be.


If you want to ensure that you only have unique items in the list, and no duplicate indexes exist, you will need additional logic to validate new entries to the list. 

As an aside, I would use TElement instead of TCollection, as the generic type refers to the elements of the collection (MyClass), not the collection itself (which is a List). Generic type names, e.g. TFoo, should be read as "type of the Foo". This applies to your TIndex (type of the index), and TElement would be similarly correct.