This entry is about a weak representability condition on (∞,1)-presheaves in E-∞ geometry. Intuitively this expresses similar behaviour as discussed at cohesion and infinitesimal cohesion, but the definitions themselves are independent and unrelated and apply in somewhat disjoint contexts.
(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
symmetric monoidal (∞,1)-category of spectra
Write $CRing_\infty^{cn}$ for the (∞,1)-category of connective E-∞ rings.
((∞,1)-presheaf on $(CRing_\infty^{cn})^{op}$) is called cohesive (Lurie Rep, def. 2.1.1) if it sends (∞,1)-fiber products of morphisms which are surjective on $\pi_0$ to (∞,1)-fiber products.
If at least those fiber products whose kernels are nilpotent ideals are preserved, then $X$ is called infinitesimally cohesive.
Infinitesimal cohesion, def. , is (together with the property that the base ring is sent to a contractible space) the defining property that makes such a functor a formal moduli problem, hence equivalently an L-∞ algebra. It is also one of the characteristics of a Deligne-Mumford stack, due to the Artin-Lurie representability theorem, hence it is satisfied by those functors which are infinitesimal approximations to geometric infinity-stacks.
Last revised on January 16, 2016 at 13:14:15. See the history of this page for a list of all contributions to it.