nLab cohesive infinity-prestack

Idea

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”.

Related concepts

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

References

• Jacob Lurie, Representability theorems (pdf)