superalgebra

and

supergeometry

# Contents

## Idea

A super vector space is an object in the monoidal category SVect: as an object it is just a ${ℤ}_{2}$-graded vector space, but when tensoring them one uses the non-trivial symmetric monoidal structure on ${ℤ}_{2}$-graded vector spaces. In simple terms, this means that when switching two ‘odd’ vectors one introduces a minus sign:

$v\otimes w↦\left(-1{\right)}^{\mathrm{deg}\left(v\right)\mathrm{deg}\left(w\right)}w\otimes v$v \otimes w \mapsto (-1)^{deg(v) deg(w)} w \otimes v

Revised on May 17, 2013 02:37:22 by Urs Schreiber (82.169.65.155)