Some Higher Coalgebra
arXiv:1508.00861
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.
This paper is being withdrawn because there is an error in the proof that Thom spectra are highly structure comodules, however the relevant Thom isomorphism and Thom diagonal results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
References in corpus (6)
- Higher Topos Theory
- Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map
- A simple universal property of Thom ring spectra
- Dualizing cartesian and cocartesian fibrations
- Factorization homology and calculus à la Kontsevich Soibelman
- Monadic approach to Galois descent and cohomology