# nLab atlas

## Theorems

#### Manifolds and cobordisms

manifolds and cobordisms

# Contents

## Idea

An atlas is a compatible collection of coordinate charts.

## Definition

In full generality, for $\mathcal{G}$ a pregeometry and $X \in Sh_{(\infty,1)}(\mathcal{G})$ an object in the (∞,1)-sheaf (∞,1)-topos, an atlas for $X$ is a collection of suitable morphisms (open maps) $\{U_i \to X\}$ with $U_i \in \mathcal{G} \hookrightarrow Sh_{(\infty,1)}(\mathcal{G})$, such that the morphism out of the coproduct

$\coprod_i U_i \to X$

is an effective epimorphism.

## Examples

### For geometric stacks

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Revised on August 18, 2013 14:24:42 by Urs Schreiber (24.131.18.91)