Some Higher Coalgebra
Algebraic Topology
2016-09-27 v4
Abstract
We define quasicategories of E_n-structured coalgebras, bialagebras and comodules. We show that: n-fold loop spaces, suspension spectra thereof, descent data for maps of E_n-ring spectra, descent corings of morphisms of E_n-ring spectra and Thom spectra are all examples of these kinds of objects. In particular, we prove that for a morphism of E_n-monoidal Kan complexes f:X->BGL_1(R), the associated Thom spectrum Mf is a structured R[X]-comodule by the classical Thom diagonal.
Cite
@article{arxiv.1508.00861,
title = {Some Higher Coalgebra},
author = {Jonathan Beardsley},
journal= {arXiv preprint arXiv:1508.00861},
year = {2016}
}
Comments
This paper is being withdrawn because there is an error in the proof that Thom spectra are highly structure comodules, however the relevant Thom isomorphism and Thom diagonal results regarding Thom spectra still hold, and appear in arXiv:1601.04123