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veit79
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$(\infty,1)$-categories and model categories

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.

veit79
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