I read several times that $(\infty,1)$-categories (weak Kan complexes, special simplicial sets) are a generalization of the concept of model categories. What does this mean? Can one associate an $(\infty,1)$-category to a model category without losing the information on the co/fibrations? How? Why is the $(\infty,1)$-category viewpoint the better one?
$(\infty,1)$-categories are equivalent to simplicial categories (categories enriched over simplicial sets). This is outlined in Lurie's higher topoi. A simplicial model category is in particular a simplicial category. Is this the way the association works? Every model category is Quillen equivalent to a simplicial model category and can thus be enriched over simplicial sets.
It would be nice if somebody could help me to clarify this.
Edit: Thank you all for the answers. It seems to me that $(\infty,1)$-categories are not a generalization of the concept of model categories. A model category is more than a category $C$ together with a class of maps $W$ such that $C[W^{-1}]$ is a category. A model structure data on a category $C$ contains the information on what a cofibration and what a fibration is. This is important for the structure. There exist different model structures with the same homotopy category as for example model structures on functor categories.
This means that if there is a kind of functor $$ F: \{\mbox{model categories}\} \to \{\mbox{($\infty,1)$-categories}\} $$ it is at least not an embedding. In spite of the answers, I still don't see how this functor (if it is really a functor) works. Where is a model category mapped to?