Axiomatic Differential Geometry I-1
Hirokazu Nishimura
TL;DR
This paper introduces an axiomatic framework for differential geometry, utilizing Weil functors, to establish a structure similar to model categories in homotopy theory.
Contribution
It presents a novel axiomatization of differential geometry that parallels the formalism of model categories, emphasizing the role of Weil functors.
Findings
Provides a new axiomatic foundation for differential geometry
Establishes parallels between differential geometry and homotopy theory
Highlights the significance of Weil functors in the axiomatization
Abstract
In this paper we give an axiomatization of differential geometry comparable to model categories for homotopy theory. Weil functors play a predominant role.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic Geometry and Number Theory