Let $\text{Cat}$ be the category of (small) categories and functors. There is a ["categorical"](http://ncatlab.org/nlab/show/canonical+model+structure+on+Cat) (also called "canonical" or "folk") model structure on $\text{Cat}$ in which the weak equivalences are the usual equivalences of categories (and as explained [here](http://sbseminar.wordpress.com/2012/11/16/the-canonical-model-structure-on-cat/), it turns out that there is a *unique* choice of cofibrations and fibrations that come with them). In this model structure, all categories are fibrant and cofibrant. 


There is also a natural question of constructing a "geometric" model structure on $\text{Cat}$ for which the weak equivalences are functros that induce weak equivalence of nerves. i.e. there is the nerve functor $N:\text{Cat}\to \text{sSet}$, where $\text{sSet}$ is the category of simplicial sets with the standard model structure, and we would like a model structure on $\text{Cat}$, for which a functor $F:C\to D$ is a weak equivalence if and only if $N(F):N(C)\to N(D)$ is a weak equivalence. There is such a construction by [Thomason](http://ncatlab.org/nlab/show/Thomason+model+structure), in which the model structure on $\text{Cat}$ is "transported" from $\text{sSet}$ along the adjunction 
$$
\tau\_1 \circ Sd^2 :\text{sSet}\leftrightarrows\text{Cat}: Ex^2\circ N
$$
Where $\tau\_1$ is the left adjoint of $N$ (sometimes called "fundamental category") and $Sd\dashv Ex$ are the barycentric subdivision / Extension adjunction of Kan. In Thomason's model structure, the cofibrations are quite complicated (they are all "Dwyer maps"). In particular a cofibrant category must be a poset.


My question is whether there exist a model structure on $\text{Cat}$, with "geometric" weak equivalences as in Thomason's, but with the same cofibrations as the "categorical" one. In other words, can we obtain a "geometric" model structure on $\text{Cat}$ by localizing the categorical one?



Constructing a "geometric" model structure on Cat by localizing the "categorical" model structure
No, there are far too many "canonical cofibrations" for that. For example, let $A$ be a category with two objects and two parallel arrows between them. Then there is a unique functor $A \to [1]$ that is injective on objects and hence a "canonical cofibration". The homotopy type of $A$ is $S^1$ so the homotopy type of the pushout of $A \to [1]$ with itself should be $S^2$, but it is $[1]$ again.


