2017/01/29 by Andrew W. Macpherson, Macpherson, Andrew W.
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1701.08359
openalex publication_date 2017/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.