Some Higher Coalgebra
Abstract
We define quasicategories of En-structured coalgebras, bialagebras and comodules. We show that: n-fold loop spaces, suspension spectra thereof, descent data for maps of En-ring spectra, descent corings of morphisms of En-ring spectra and Thom spectra are all examples of these kinds of objects. In particular, we prove that for a morphism of En-monoidal Kan complexes f:X->BGL1(R), the associated Thom spectrum Mf is a structured R[X]-comodule by the classical Thom diagonal.
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