Day Convolution, Goodwillie Derivatives and the Lie Operad

Michael Ching, Amherst College

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Passcode: 998749

Quillen's approach to rational homotopy and recent work of Heuts on chromatic homotopy reveal a central role for Lie algebras in encoding topological spaces. One explanation for this role, exploited by Heuts, comes from Goodwillie calculus where the derivatives of the identity functor can be identified with a version of the Lie operad. In this talk I will describe a new construction of those derivatives that explains directly how the operad structure arises, and which applies to the derivatives of the identity functor on other categories too. That construction is based on Day convolution of functors between certain symmetric monoidal categories.