$\infty$-categorical monadicity and descent
Category Theory
2016-09-20 v1 Algebraic Topology
Abstract
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.
Cite
@article{arxiv.1609.05642,
title = {$\infty$-categorical monadicity and descent},
author = {Yuri J. F. Sulyma},
journal= {arXiv preprint arXiv:1609.05642},
year = {2016}
}