Monoidally graded manifolds

Abstract

We give a generalization of the theory of ${\mathbb{Z}}_2$-graded manifolds to a theory of $\mathcal{I}$-graded manifolds, where $\mathcal{I}$ is a commutative semi-ring with some additional properties. We prove Batchelor's theorem in this generalized setting. To our knowledge, such a proof is still missing except for some special cases.

16 pages; to appear in J. Geom. Phys

References in corpus (1)

• Mathematical structures of cohomological field theories

Cited by in corpus (3)

• Mathematical structures of cohomological field theories
• Normal forms of $\mathbb{Z}$-graded $Q$-manifolds
• $H$-covering of a supermanifold