Highly Structured Coalgebras and Comodules

The thesis studies coalgebras and comodules in higher categories. Rigidification results compare homotopy coherent objects with their strict analogues and we prove that it is not possible to rigidify coalgebras in spectra. However, we also show that comodules in connective modules over the Eilenberg-Mac Lane spectrum over a field can be rigidified if the coalgebra is simply connected and strict. This allows to define the notion of derived cotensor product of comodules