2021/08/30 by Alexei Kotov, Kotov, Alexei, Vladimir Salnikov +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2108.13496
openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss the categorical properties of ℤ-graded manifolds. We start by describing the local model paying special attention to the differences in comparison to the ℕ-graded case. In particular we explain the origin of formality for the functional space and spell-out the structure of the power series. Then we make this construction intrinsic using filtrations. This sums up to proper definitions of objects and morphisms in the category. We also formulate the analogue of Batchelor's theorem for the global structure of ℤ-graded manifolds.