I would like to know how to cite this theorem (which has a quite surprising consequence):



> 
> A model category $\mathcal{M}$ is right proper if and only if for any
>  weak equivalence $f:A\to B$, the Quillen adjunction
>  $\Sigma\_f:\mathcal{M}/ A \leftrightarrows \mathcal{M} / B:f^\*$ is a Quillen equivalence.
> 
> 
> 


I had never heard of it (I never read that in any textbook I believe) before I browse the [nLab site](http://ncatlab.org/nlab/show/proper+model+category) which refers to this [blog comment](http://golem.ph.utexas.edu/category/2012/05/the_mysterious_nature_of_right.html#c041294) from C. Rezk. 



Characterization of right properness using slice categories
This is Proposition 2.7 in Rezk's [*Every Homotopy Theory of Simplicial Algebras Admits a Proper Model*](http://arxiv.org/abs/math/0003065v1)


