[Wikipedia](http://en.wikipedia.org/wiki/Symmetric_monoidal_category) states:



> 
> The classifying space (geometric realization of the nerve) of a symmetric monoidal category is an infinite loop space.
> 
> 
> 


If my mind is correct, Segals delooping machine gives a functor $Sp$ from topological symmetric monoidal categories $C$ to prespectra (In this question, a presepectrum is a sequence of based spaces $X\_0,X\_1$,... with structure maps $\Sigma X\_i\rightarrow X\_{i+1}$) with $Sp(C)\_0=BC$ the classifying space of the category. 


If I remember correctly, one of Segals results is that the adjoints of the structure maps $Sp(C)\_i\rightarrow \Omega Sp(C)\_{i+1}$ are weak homotopy equivalences for $i\ge1$ and for $i=1$ this is the case iff $\pi\_0(Sp(C)\_0)=\pi\_0(BC)$ is an abelian group with the induced multiplication which comes from the fact that $BC$ is a commutative monoid up to homotopy.


So the classifying space of a topological symmetric monoidal category $C$ can in this sense infinitely delooped only if $\pi\_0(BC)$ is a group.


I ask myself:


1.) Did I say anything stupid or wrong?


2.) Is Wikipedia wrong?



Is the classifying space of a symmetric monoidal category an infinite loop space?
You need group Completion, indeed. 


