Infinite-Dimensional and Colored Supermanifolds

Here the theory of finite-dimensional supermanifolds is generalized in two directions. First, we introduce infinite-dimensional locally isomorphic to arbitrary Banach (or, more generally, convex) superspaces. This achieved by considering as functors (equipped with some additional structure) from category Grassmann superalgebras into corresponding smooth manifolds (Banach or convex). Selected examples: flag superspaces well unitary supergroups Hilbert Second, define supermanifolds, -graded spaces. These are referred what follows (super stringsol;)k-manifolds, colored manifolds). The superfields (i.e., morphisms coordinate ring) describing, hopefully, particles general statistics than Bose + Fermi, turn out have, general, an infinite number components.