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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 23rd 2014
   • (edited Sep 23rd 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to _[[group completion]]_ a paragraph with minimum pointers to the traditional construction $\Omega B (-)$ as group completion of topological monoids. Added a corresponding brief paragraph to _[[K-theory of a permutative category]]_ (where this had been missing). What is still missing (on the $n$Lab and maybe generally in the literature) is a really clear statement that this is indeed a model for the $\infty$-categorical group completion operation which is invoked at _[[K-theory of a symmetric monoidal (infinity,1)-category]]_. One place where such a derived functor statement is made is [Dwyer-Kan 80, remark 9.7](http://ncatlab.org/nlab/show/group+completion#DwyerKan80) (thanks to Charles Rezk's MO comment [here](http://mathoverflow.net/a/17135/381)). I have added pointers to that to the relevant entries, but this ought to be sorted out in more detail.

   added to group completion a paragraph with minimum pointers to the traditional construction $\Omega B (-)$ as group completion of topological monoids. Added a corresponding brief paragraph to K-theory of a permutative category (where this had been missing).

   What is still missing (on the $n$Lab and maybe generally in the literature) is a really clear statement that this is indeed a model for the $\infty$-categorical group completion operation which is invoked at K-theory of a symmetric monoidal (infinity,1)-category.

   One place where such a derived functor statement is made is Dwyer-Kan 80, remark 9.7 (thanks to Charles Rezk’s MO comment here). I have added pointers to that to the relevant entries, but this ought to be sorted out in more detail.