Integrating morphisms of Lie 2-algebras

DOI10.1112/S0010437X1200067XzbMath1315.22023arXiv0910.1818MaRDI QIDQ4911104

Behrang Noohi

Publication date: 13 March 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1818

zbMATH Keywords

Lie 2-algebrasMorita morphismscrossed modules of Lie algebrasconnected coverbutterfliesLie 2-groupsL-infinity algebrascrossed modules of Lie groupshomotopy fiber of a butterflyintegration of Lie 2-algebra morphismsweak morphisms

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40) Other generalizations of groups (20N99)

Related Items (10)

Hom-Leibniz 2-algebras ⋮ Multiplicative vector fields on bundle gerbes ⋮ Butterflies in a semi-abelian context ⋮ On the homotopy theory for Lie \(\infty\)-groupoids, with an application to integrating \(L_\infty\)-algebras ⋮ Infinitesimal symmetries of bundle gerbes and Courant algebroids ⋮ Lie 2-algebras of vector fields ⋮ Hom-Lie 2-superalgebras ⋮ Symmetric homotopy theory for operads ⋮ Gerbes in geometry, field theory, and quantisation ⋮ On the Lie 2-algebra of sections of an \(\mathcal{LA}\)-groupoid

Cites Work

• Homotopy types of topological stacks
• Modules croisés généralisés de longueur 2
• Three-crossed modules
• Butterflies. I: Morphisms of 2-group stacks
• Lie theory for nilpotent \(L_{\infty}\)-algebras
• Integrating -algebras
• Algebraic Models of 3‐Types and Automorphism Structures for Crossed Modules
• Local geometric Langlands correspondence and affine Kac-Moody algebras

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