Thanks Keith. That was my line of thinking as well, yet, there must be something wrong with my arguments as the theorem provides a construction which guarantees a left adjoint.

My question is: what's wrong?

It is either that the example above does not satisfy the settings of the theorem, or that I have a mistake in the calculations (or both... ;-)). But I can't seem to find either.

My question is: what's wrong?

It is either that the example above does not satisfy the settings of the theorem, or that I have a mistake in the calculations (or both... ;-)). But I can't seem to find either.