A Comparison of the functors of points of Supermanifolds
L. Balduzzi, C. Carmeli, R. Fioresi
TL;DR
This paper investigates the functor of points and Weil--Berezin functor for supermanifolds, providing characterization theorems, discussing representability, and exploring applications to differential calculus.
Contribution
It offers a comprehensive analysis of the functorial approach to supermanifolds, including new characterization theorems and insights into representability and differential calculus applications.
Findings
Characterization theorems for functor of points and Weil--Berezin functor
Discussion on representability issues of supermanifolds
Applications to differential calculus and transitivity theorems
Abstract
We study the functor of points and the local functor of points (here called the Weil--Berezin functor) for smooth and holomorphic supermanifolds, providing characterization theorems and fully discussing the representability issues. In the end we examine applications to differential calculus including the transitivity theorems.
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Taxonomy
TopicsNonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra