$\infty$-categorical monadicity and descent

Yuri J. F. Sulyma

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arXiv · 1609.05642

$\infty$-categorical monadicity and descent

Yuri J. F. Sulyma

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Abstract

Riehl and Verity have introduced an "$\infty$-cosmic" framework in which they redevelop the category theory of $\infty$-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 $\infty$-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.

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Yuri J. F. Sulyma. 2016-09-19. $\infty$-categorical monadicity and descent. https://arxiv.org/abs/1609.05642

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