Slices of infinity sheaves - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T09:37:39Z http://mathoverflow.net/feeds/question/58861 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58861/slices-of-infinity-sheaves Slices of infinity sheaves David Carchedi 2011-03-18T18:06:00Z 2012-01-20T14:09:08Z <p>I know from classical category theory that if $C$ is a small category and $X$ is a presheaf, that there is a canonical equivalence $$Set^{C^{op}}/X \simeq Set^{\left(C/X\right)^{op}},$$ where $C/X$ is the category of elements of $X$ (i.e. the Grothendieck construction of $X$). Moreover, if $C$ carries a Grothendieck topology, this statement is true for sheaves, where $C/X$ inherits a canonical topology from $C$.</p> <p>Can I make a similar statement if I go to infinity sheaves, and if so, does anyone have a reference? Thanks. If someone knows a way of proving this model theoretically, that would also be nice.</p> http://mathoverflow.net/questions/58861/slices-of-infinity-sheaves/86209#86209 Answer by David Carchedi for Slices of infinity sheaves David Carchedi 2012-01-20T14:09:08Z 2012-01-20T14:09:08Z <p>This is Corollary 5.1.6.12 in HTT. Somehow I overlooked this.</p>