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arXiv · 0706.0531

Ring completion of rig categories

Nils A. Baas·Bjorn Ian Dundas·Birgit Richter·John Rognes
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Abstract

We offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). Given a rig category R we construct a natural additive group completion R' that retains the multiplicative structure, hence has become a ring category. If we start with a commutative rig category R (also known as a symmetric bimonoidal category), the additive group completion R' will be a commutative ring category. In an accompanying paper we show how this can be used to prove the conjecture from [BDR] that the algebraic K-theory of the connective topological K-theory spectrum ku is equivalent to the algebraic K-theory of the rig category V of complex vector spaces.

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Nils A. Baas, Bjorn Ian Dundas, Birgit Richter, John Rognes. 2007-06-04. Ring completion of rig categories. https://doi.org/10.1515/crelle.2012.024

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