Supersmooth topoi (Q1590863)

Synthetic Differential Supergeometry (SDSG) should be of interest not only in the subject of nonconmutative geometry but also for better understanding of the boson-fermion interplay in particle physics. Its set-up has been supersmooth supermanifolds but various definitions of them appeared, as well as how many generators the Grassmann algebra at issue should have. On the other hand, holomorphic functions in complex spaces may be nilpotent and so visible from a synthetic viewpoint. The author continues his previous work, the main objective being here a good enough model of SDSG which is a Grothendieck topos containing the category of \(G^\infty\)-supermanifolds and \(G^\infty\)-mappings as a full subcategory, first also generalizing the clasical notion of complex space. His constructions are based on Dubuc and Taubin algebraic theory of analytic rings [\textit{E.Dubuc} and \textit{G. Taubin}, Cah. Topologie Géom. Différ. 24, No.~3, 225-265 (1983; Zbl 0575.32004)].