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Tuesday, December 5, 2017

**Abstract:** The Grothendieck group K_0 of a commutative ring is well-known to be a lambda-ring, via taking exterior powers of modules. In joint work in progress with Barwick, Glasman, and Nikolaus, we study space-level refinements of this structure. Namely, we show that the K-theory space of a category is naturally functorial for polynomial functors, and describe a universal property of the extended K-theory functor. This leads to a natural spectral refinement of the notion of a lambda-ring.