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## Categorical proof of Holomorphic Atiyah-Bott formula

Journal of the Institute of Mathematics of Jussieu. 2020. Vol. 19. No. 5. P. 1739-1763.

Given a symmetric monoidal (∞,2)-category ℰ we promote the trace construction to a functor. We then apply this formalism to the case when ℰ is the (∞,2)-category of k-linear presentable categories which in combination of various calculations in the setting of derived algebraic geometry gives a categorical proof of the classical Atiyah-Bott formula (also known as the Holomorphic Lefschetz fixed point formula).