nLab
super smooth set

Context

Geometry

Super-Geometry

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

A\phantom{A}(higher) geometryA\phantom{A}A\phantom{A}siteA\phantom{A}A\phantom{A}sheaf toposA\phantom{A}A\phantom{A}∞-sheaf ∞-toposA\phantom{A}
A\phantom{A}discrete geometryA\phantom{A}A\phantom{A}PointA\phantom{A}A\phantom{A}SetA\phantom{A}A\phantom{A}Discrete∞GrpdA\phantom{A}
A\phantom{A}differential geometryA\phantom{A}A\phantom{A}CartSpA\phantom{A}A\phantom{A}SmoothSetA\phantom{A}A\phantom{A}Smooth∞GrpdA\phantom{A}
A\phantom{A}formal geometryA\phantom{A}A\phantom{A}FormalCartSpA\phantom{A}A\phantom{A}FormalSmoothSetA\phantom{A}A\phantom{A}FormalSmooth∞GrpdA\phantom{A}
A\phantom{A}supergeometryA\phantom{A}A\phantom{A}SuperFormalCartSpA\phantom{A}A\phantom{A}SuperFormalSmoothSetA\phantom{A}A\phantom{A}SuperFormalSmooth∞GrpdA\phantom{A}

Last revised on June 25, 2018 at 08:51:45. See the history of this page for a list of all contributions to it.