nLab
formal smooth set

Contents

Idea

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.

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}

Created on June 25, 2018 at 08:50:57. See the history of this page for a list of all contributions to it.