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Let p be a prime number. We compute the Yoneda extension algebra of GL2 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 GL2 over such a field

Koszul dual $$2$$ 2 -functors and extension algebras of simple modules for $$GL_2$$ G L 2