Let $W$ be a family of arrows in a category $\mathcal{C}$, there is a nature notion of localisation w.r.t. $W$. And if $W$ satisfies some nice properties, we have calculus of fraction. 


Now consider a quasi-category(i.e., weak Kan complex) $\mathcal{C}$, in which every $k$-arrows are invertible if $k>1$. Given a family of $1$-arrows $W$, is there a notion of localisation w.r.t. $W$, that is a universal way to invert all arrows in $W$? Furthermore, if $W$ is nice enough, does the notion of the calculus of fraction have a sensible generalization?


When I search localisation + quasicategory online, it yields mostly simplicial Localisation, Hammock localisation...which state how to localise a category rather than a quasi-catgory.



Localisation in a quasi-category 
Some aspects and plenty of further pointers (mostly to Jacob Lurie's book, of course) are collected here:


<http://ncatlab.org/nlab/show/localization+of+an+(infinity,1)-category>


<http://ncatlab.org/nlab/show/reflective+sub-(infinity,1)-category>


