M Theory Lesson 95

The classic paper on Koszul duality for operads is [1]. It is very difficult for a physicist to follow, but let us make a note on a remark on page 3. They interpret the duality for operads in terms of a dualising functor hom(-,Lie) where Lie is the operad associated to Lie algebras.

This is like the behaviour of schizophrenic objects, meaning in this case the object Lie. A more classical example is the object U(1) underlying Pontrjagin duality.

[1] V. Ginzburg and M. Kapranov, Duke Math. J. 76, 1 (1994) 203-272