# The universal property of derived geometry

@article{Macpherson2017TheUP, title={The universal property of derived geometry}, author={Andrew W. Macpherson}, journal={arXiv: Category Theory}, year={2017} }

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…

## 2 Citations

An alternative to hypercovers

- Mathematics
- 2020

I introduce a class of diagrams in a Grothendieck site called "atlases" which can be used to study hyperdescent, and show that hypersheaves take atlases to limits using an indexed `nerve'…

On the Universal Property of Derived Manifolds

- Mathematics
- 2019

It is well known that any model for derived manifolds must form a higher category. In this paper, we propose a universal property for this higher category, classifying it up to equivalence. Namely,…

## References

SHOWING 1-10 OF 27 REFERENCES

Derived manifolds and Kuranishi models

- Mathematics
- 2012

A model structure is defined on the category of derived differentiable schemes, and it is used to analyse the truncation 2-functor from derived manifolds to d-manifolds. It is proved that the induced…

Affine manifolds are rigid analytic spaces in characteristic one, I

- Mathematics
- 2015

I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms.
The…

Models for smooth infinitesimal analysis

- Mathematics
- 1990

The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of…

Homotopical Algebraic Geometry II: Geometric Stacks and Applications

- Mathematics
- 2004

This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative…

Au-dessous de SpecZ .

- Mathematics
- 2009

In this article we use the theories of relative algebraic geometry and of homotopical algebraic geometry (cf. [HAGII]) to construct some categories of schemes defined under Spec ℤ. We define the…

Homological Algebra for Superalgebras of Differentiable Functions

- Mathematics
- 2012

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we…

Derived smooth manifolds

- Mathematics
- 2008

We define a simplicial category called the category of derived manifolds. It contains the category of smooth manifolds as a full discrete subcategory, and it is closed under taking arbitrary…

Derived Algebraic Geometry V: Structured Spaces

- Mathematics
- 2009

In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their…

On manifolds with corners

- Mathematics
- 2012

Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received…