Covariance and Contravariance on the same type argument

Question

The C# spec states that an argument type cannot be both covariant and contravariant at the same time.

This is apparent when creating a covariant or contravariant int

Answer 1

Is this limitation simply a language specific constraint or are there deeper, more fundamental reasons based in category theory that would make you not want your type to be both covariant and contravariant?

No, there is a much simpler reason based in basic logic (or just common sense, whichever you prefer): a statement cannot be both true and not true at the same time.

Covariance means S <: T ⇒ G <: G and contravariance means S <: T ⇒ G <: G. It should be pretty obvious that these can never be true at the same time.