The simplest example of Koszul duality (see introduction of http://www.ams.org/journals/jams/1996-9-02/S0894-0347-96-00192-0/)

Let $V = \mathbb{C}x$ be a $1$ dimensional vector space. Then the exterior algebra is $A=\mathbb{C}[x]/(x^2)$, and the symmetric algebra is $A^! = \mathbb{C}[x]$. Koszul duality states that there exists an isomorphism (where "mod" means the category of finitely generated modules):

$F: D^b(A-mod) \rightarrow D^b(A^!-mod)$

The heart of the category on the left is $A-mod$; what is the image of this on the right? It should be possible to work this out by working through the above paper, but there are many things in that paper which I don't understand (and this toy example should be easy).