A Quillen's Theorem A for strict infinity-categories I: The simplicial proof

作者：Ara Dimitri^*; Maltsiniotis Georges

来源：Advances in Mathematics, 2018, 328: 446-500.

DOI：10.1016/j.aim.2018.01.018

• Strict infinity-categories
• Augmented directed complexes
• Street's nerve
• Gray tensor product
• Theorem A
• Slices

The aim of this paper is to prove a generalization of the famous Theorem A of Quillen for strict infinity-categories. This result is central to the homotopy theory of strict infinity-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 infinity-categorical methods.

• 出版日期2018-4-13