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- Title
∞-categorical monadicity and descent.
- Authors
Sulyma, Yuri J. F.
- 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.
- Subjects
FUNCTOR theory; DESCENT groups; THEORY of descent (Mathematics); CATEGORIES (Mathematics); ADJUNCTION theory; MATHEMATICAL sequences
- Publication
New York Journal of Mathematics, 2017, Vol 23, p749
- ISSN
1076-9803
- Publication type
Article