Geometric higher groupoids and categories

Abstract

In an enriched setting, we show that higher groupoids and higher categories form categories of fibrant objects. The nerve of a differential graded algebra is a higher category in the category of algebraic varieties, where covers are defined to be smooth epimorphisms.

Proofs of Lemma 4.2 and Lemma 6.2 repaired, and other small changes

References in corpus (2)

• Higher Topos Theory
• Un schéma simplicial de Grothendieck-Pridham

Cited by in corpus (4)

• Maurer-Cartan moduli and theorems of Riemann-Hilbert type
• On the homotopy theory for Lie $\infty$-groupoids, with an application to integrating $L_{\infty }$-algebras
• Principal actions of stacky Lie groupoids
• Higher Vector Bundles