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A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof
- Source :
- Advances in Mathematics, Advances in Mathematics, Elsevier, 2018, 328, pp.446-500. ⟨10.1016/j.aim.2018.01.018⟩, Advances in Mathematics, 2018, 328, pp.446-500. ⟨10.1016/j.aim.2018.01.018⟩
- Publication Year :
- 2018
- Publisher :
- HAL CCSD, 2018.
-
Abstract
- 51 pages, in French, v2: extended introduction, journal version; International audience; The aim of this paper is to prove a generalization of the famous Theorem A of Quillen for strict $\infty$-categories. This result is central to the homotopy theory of strict $\infty$-categories developed by the authors. The proof presented here is of a simplicial nature and uses Steiner's theory of augmented directed complexes. In a subsequent paper, we will prove the same result by purely $\infty$-categorical methods.
Details
- Language :
- French
- ISSN :
- 00018708 and 10902082
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics, Advances in Mathematics, Elsevier, 2018, 328, pp.446-500. ⟨10.1016/j.aim.2018.01.018⟩, Advances in Mathematics, 2018, 328, pp.446-500. ⟨10.1016/j.aim.2018.01.018⟩
- Accession number :
- edsair.doi.dedup.....cc9360affb4552abc2ba834ba33ea734