Ring completion of rig categories

Details Ring completion of rig categories Ring completion of rig categories

2007-06-04

arxiv.org/abs/0706.0531v4

Mathematics

K-Theory and Homology

There was a mathematical error in arXiv:0706.0531v2: the map T in the purported proof of Lemma 3.7(2) is not well defined. Ver

Scientific paper

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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