Categories of supermanifolds

Abstract

The category of G-supermanifolds [BB1,BBH] provides a consistent and concrete model for the development of supergeometry. In order to supply proper motivations for the introduction of these objects, and also for historical reasons, we shall start with a brief description of graded manifolds; these were originally introduced by Berezin and Leĭtes [BL, Leĭ], although the most extensive treatment can be found in Kostant [Kos] and Manin [Ma2]. Graded manifolds also play a direct role in the theory developed in this book, in that some results holding in that category can be either reformulated or applied as they are in the context of G-supermanifolds.

Nous avons vu tant de monstres de cette espèce que nous sommes un peu blasés, et qu’il faut accumuler les caractères tératologiques les plus biscornus pour arriver encore à nous étonner N. Bourbaki