cohesive infinity-prestack

In Lurie 12, def. 2.1.1 an ∞-prestack $\mathcal{C}^{op} \to$ ∞Grpd is called *cohesive* if it sends (∞,1)-fiber products of “essentially surjective” maps (in the opposite (∞,1)-category of the (∞,1)-site $\mathcal{C}$) to $(\infty,1)$-fiber products in ∞Grpd. It is called *infinitesimally cohesive* (Lurie 12, def. 2.1.1) if this property holds at least for fiber products of maps with “infinitesimal kernel”.

This is *un-related* to the notion of *cohesive (∞,1)-topos*.

- Jacob Lurie,
*Representability theorems*(pdf)