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Tuesday, October 24, 2017

**Abstract:** What sorts of categories can K-theory be defined for? We know that exact categories and Waldhausen categories can be used as appropriate input. However, there are geometric categories where we would like to define K-theory where we are only allowed to ``cut and paste" rather than quotient --- examples of these include the category of varieties, and the category of polytopes. I'll define a more general context where one may talk about the algebraic K-theory of these categories, and outline a proof of a general version of Quillen's devissage. I'll outline applications to studying "derived motivic measures" and the scissors congruence problem. This is joint work with Inna Zakharevich.