higher geometry / derived geometry
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
function algebras on ∞-stacks?
derived smooth geometry
The concept of formal smooth set is a kind of generalized space generalizing smooth sets from plain differential geometry to differential geometry equipped with explicit infinitesimal spaces, hence to synthetic differential geometry. Just as a smooth set is equivalently a sheaf on the site of Cartesian spaces, so a formal smooth set is a sheaf on the site of formal Cartesian spaces, hence of Cartesian products of Cartesian spaces with infinitesimally thickened points. The resulting sheaf topos is also known as Dubuc’s Cahiers topos.
For the moment, for more see at geometry of physics the chapters manifolds and orbifolds and geometry of physics – supergeometry.
$\phantom{A}$(higher) geometry$\phantom{A}$ | $\phantom{A}$site$\phantom{A}$ | $\phantom{A}$sheaf topos$\phantom{A}$ | $\phantom{A}$∞-sheaf ∞-topos$\phantom{A}$ |
---|---|---|---|
$\phantom{A}$discrete geometry$\phantom{A}$ | $\phantom{A}$Point$\phantom{A}$ | $\phantom{A}$Set$\phantom{A}$ | $\phantom{A}$Discrete∞Grpd$\phantom{A}$ |
$\phantom{A}$differential geometry$\phantom{A}$ | $\phantom{A}$CartSp$\phantom{A}$ | $\phantom{A}$SmoothSet$\phantom{A}$ | $\phantom{A}$Smooth∞Grpd$\phantom{A}$ |
$\phantom{A}$formal geometry$\phantom{A}$ | $\phantom{A}$FormalCartSp$\phantom{A}$ | $\phantom{A}$FormalSmoothSet$\phantom{A}$ | $\phantom{A}$FormalSmooth∞Grpd$\phantom{A}$ |
$\phantom{A}$supergeometry$\phantom{A}$ | $\phantom{A}$SuperFormalCartSp$\phantom{A}$ | $\phantom{A}$SuperFormalSmoothSet$\phantom{A}$ | $\phantom{A}$SuperFormalSmooth∞Grpd$\phantom{A}$ |
Created on June 25, 2018 at 08:50:57. See the history of this page for a list of all contributions to it.