### Abstract

We show that for a differential graded Lie algebra g whose components vanish in degrees below −1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V. Hinich [Hinich, 1997].

Original language | English (US) |
---|---|

Article number | 29 |

Pages (from-to) | 1001-1016 |

Number of pages | 16 |

Journal | Theory and Applications of Categories |

Volume | 30 |

State | Published - Jul 7 2015 |

### Fingerprint

### Keywords

- Groupoid
- L∞-algebra
- Simplicial nerve

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*Theory and Applications of Categories*,

*30*, 1001-1016. [29].

}

*Theory and Applications of Categories*, vol. 30, 29, pp. 1001-1016.

**Deligne groupoid revisited.** / Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Deligne groupoid revisited

AU - Bressler, Paul

AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris L

PY - 2015/7/7

Y1 - 2015/7/7

N2 - We show that for a differential graded Lie algebra g whose components vanish in degrees below −1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V. Hinich [Hinich, 1997].

AB - We show that for a differential graded Lie algebra g whose components vanish in degrees below −1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V. Hinich [Hinich, 1997].

KW - Groupoid

KW - L∞-algebra

KW - Simplicial nerve

UR - http://www.scopus.com/inward/record.url?scp=84937440626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937440626&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 1001

EP - 1016

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

SN - 1201-561X

M1 - 29

ER -