Ring completion of rig categories
K-Theory and Homology
2022-06-22 v4 Algebraic Topology
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.
Cite
@article{arxiv.0706.0531,
title = {Ring completion of rig categories},
author = {Nils A. Baas and Bjorn Ian Dundas and Birgit Richter and John Rognes},
journal= {arXiv preprint arXiv:0706.0531},
year = {2022}
}