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A theorem of Deligne suggests that the complex numbers are not algebraically closed in a 1-categorical sense but that their 1-categorical algebraic closure is the category sVec of complex super vector spaces. In fact, this property uniquely (up to non-unique isomorphism) characterizes sVec amongst complex-linear symmetric monoidal categories. In these talks, we will outline work in progress on constructing complex-linear symmetric n-categories which are higher categorical analogues of sVec in that they are uniquely characterized by being the n-categorical separable closure of the complex numbers. We will explore the resulting higher-categorical absolute Galois group of the complex numbers, and outline a construction of that group very much akin to the surgery-theoretic description of the stable piecewise linear group PL.