Flatness for infinity functors - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T17:30:57Z http://mathoverflow.net/feeds/question/83350 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83350/flatness-for-infinity-functors Flatness for infinity functors David Carchedi 2011-12-13T16:53:06Z 2012-04-27T10:24:15Z <p>It is well known that for ordinary categories, if $C$ has finite limits and $D$ is cocomplete, and $A:C \to D$ is left-exact (i.e. preserves finite limits) then the left-Kan extension of $F$ along the Yoneda embedding $y:C \hookrightarrow Set^{C^{op}}$ is left-exact. I'm pretty sure this is still true for $\left(\infty,1\right)$-categories, once we replace the role of presheaves with that of $\infty$-presheaves, but is this written up somewhere?</p> http://mathoverflow.net/questions/83350/flatness-for-infinity-functors/95343#95343 Answer by David Carchedi for Flatness for infinity functors David Carchedi 2012-04-27T10:24:15Z 2012-04-27T10:24:15Z <p>For reference, at least when $D$ is an infinity topos, which I believe is probably necessary, this is Proposition 6.1.5.2 in HTT.</p>