# nLab representable morphism of stacks

Contents

### Context

#### $(\infty,1)$-Topos Theory

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Definition

A morphism $f : X \to Y$ of stacks over a site $C$ is called representable if for all representable objects $U \in C \stackrel{Y}{\hookrightarrow} Stacks(C)$ and all morphisms $U \to Y$ the homotopy pullback $X \times_Y U$ in

$\array{ X \times_Y U &\to& X \\ \downarrow &{}^{\simeq}\swArrow& \downarrow^f \\ U &\to& Y }$

is again representable.

## Properties

### Push-forward in generalized cohomology

Along representable morphisms $f$ of stacks over smooth manifolds (smooth infinity-groupoids) is induced a push-forward in generalized cohomology operation.

## References

The general definition appears for instance as def. 38.5 in

(there with stacks perceived equivalently and dually under the Grothendieck construction as fibered categories).

Applications of push-forward in generalized cohomology along representable morphisms appear for instance in

Last revised on November 7, 2012 at 21:53:48. See the history of this page for a list of all contributions to it.