English

The universal property of derived geometry

Category Theory 2021-04-02 v3 Algebraic Geometry Differential Geometry

Abstract

Derived geometry can be defined as the universal way to adjoin finite homotopical limits to a given category of manifolds compatibly with products and glueing. The point of this paper is to show that a construction closely resembling existing approaches to derived geometry in fact produces a geometry with this universal property. I also investigate consequences of this definition in particular in the differentiable setting, and compare the theory so obtained to D. Spivak's axioms for derived C-infinity geometry.

Keywords

Cite

@article{arxiv.1701.08359,
  title  = {The universal property of derived geometry},
  author = {Andrew W. Macpherson},
  journal= {arXiv preprint arXiv:1701.08359},
  year   = {2021}
}

Comments

The reasoning in the paper in its present form is inadequate to support its conclusions. After some effort to revise it, I have decided that the best approach is to withdraw it and develop the material instead as several smaller projects

R2 v1 2026-06-22T18:03:17.614Z