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supersymmetry

# Contens

## Idea

Just as a smooth set is a generalized smooth space in differential geometry modeled as a sheaf on the category of Cartesian spaces with smooth functions between them, so a super smooth set is a sheaf on the category of super Cartesian spaces, being a generalized space in supergeometry.

Since super smooth sets contain infinitesimal spaces, it makes good sense to make this explicit and consider super formal smooth sets right away, hence sheaves on super formal Cartesian spaces

For details see at geometry of physics – supergeometry.

geometries of physics

$\phantom{A}$(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}$

Last revised on August 1, 2018 at 08:05:05. See the history of this page for a list of all contributions to it.