Some Higher Coalgebra

Jonathan Beardsley

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arXiv · 1508.00861

Some Higher Coalgebra

Jonathan Beardsley

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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.

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Jonathan Beardsley. 2015-08-04. Some Higher Coalgebra. https://arxiv.org/abs/1508.00861

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