F# equivalent of the C# 'object' keyword

In C# object is just a type name referring to System.Object. In F#, you can either use this full .NET name or a type alias obj.

Now, regarding a field declaration - there are various ways to write that depending on the context. Also, it is a good practice to initialize all fields in F#, so it would be useful to see larger context of your code.

However, you may write this:

type A() = 
  let mutable (myInnerObj:obj) = null

This creates a private field myInnerObj of type System.Object initialized to null, which is mutable can can be assigned later (myInnerObj <- new Random(), for example). I used example with private field, because public fields are generally discouraged in .NET.

@Tomas is right. You may also want to check out these blogs:

The basic syntax of F# - types

What does this C# code look like in F#?