New York Journal of Mathematics
Volume 23 (2017) 749-777


Yuri J. F. Sulyma

∞-categorical monadicity and descent

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Published: June 16, 2017
Keywords: Infinity-categories, monadicity, descent, Barr-Beck, spectral sequences
Subject: 18G55, 55U35, 55U40 (Primary) 18A40, 18G30, 18G40 (Secondary)

Riehl and Verity have introduced an "∞-cosmic'' framework in which they redevelop the category theory of ∞-categories using 2-categorical arguments. In this paper, we begin with a self-contained review of the parts of their theory needed to discuss adjunctions and monadicity. This is applied in order to extend to the ∞-categorical context the classical criterion for fully faithfulness of the comparison functor induced by an adjunction. We discuss the relation with previous work in the literature--which primarily uses model-categorical techniques--and indicate applications to descent theory.


Sulyma was supported in part by NSF grant DMS-1564289

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University of Texas, Austin, TX 78712