Year: 2016
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Sulyma, Yuri J. F.
Institution: The University of Texas at Austin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2521937460