superalgebra and (synthetic ) supergeometry Supergeometry is the (higher) geometry over the base topos on superpoints modeled on the canonical line object in there. As ordinary differential geometry studies spaces – smooth manifolds – that locally look like vector spaces, supergeometry studies spaces – supermanifolds – that locally look like super vector spaces. As ordinary algebraic geometry studies spaces – schemes – that locally look like affine spaces, supergeometry studies...