Year: 2026
Type: preprint
Abstract: We give an axiomatic homotopical analog of the classical categorical Beck monadicity theorem. It often holds when classical monadicity fails. This grew out of an understanding of a general context for recognition principles in iterated loop space theory, as treated in the logical sequel ArXiv 2402.03649, but the present result applies differently and more generally. An example gives a new perspective on the old equivalence between simplicial sets and topological spaces: both are equivalent to simplicial topological spaces, and the equivalence implies a curiously close relationship between realizations of simplicial spaces and realizations of their underlying simplicial sets, viewed as discrete simplicial spaces.
Source: arXiv (Cornell University)
Authors: Kong, Hana Jia, May, J. Peter, Zou, Foling
Institution: Zhejiang University
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168427256
Cites:
Cited by:
Related to: