Koszul dual 2-functors and extension algebras of simple modules for   $GL_2$
  Let p be a prime number. We compute the Yoneda extension algebra of $GL_2$ over an algebraically closed field of characteristic p by developing a theory of Koszul duality for a certain class of 2-functors, one of which controls the category of rational representations of $GL_2$ over such a field. 
Vanessa Miemietz, Will Turner
math.RT