# nLab sheaf of L-∞ algebras

Contents

## Examples

### $\infty$-Lie algebras

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

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Idea

A sheaf of $L_\infty$-algebras is a suitable sheaf/stack/∞-stack of L-∞ algebras/dg-Lie algebras.

These structures appear in the deformation theory of the given base space/site: where a single L-∞ algebra is equivalently a formal moduli problem (hence “over the point), so a sheaf of these over some base $X$ may be thought of as an $X$-parameterized formal moduli problem (eg. Hinich 03).

## References

Discussion in the context of deformation theory/parameterized formal moduli problems is in

Quasi-coherent sheaves of dg-Lie algebras appear in

Discussion in physics, of sheaves of $L_\infty$-algebras of physical fields in prequantum field theory includes

Created on January 3, 2014 at 16:24:20. See the history of this page for a list of all contributions to it.