nLab model structure on coalgebras over a comonad

Idea

model category structures on Eilenberg-Moore categories of coalgebras over a comonad.

Related concepts

• model stucture on dg-coalgebras, model structure on dg-comodules

• model structure on monoids in a monoidal model category

• model structure on algebras over an operad

• model structure on coalgebras over a comonad

• model structure on simplicial T-algebras

References

Sufficient conditions for the exstence of a model structure on coalgebras over a comonad are stated as theorem 5.8 in

• Kathryn Hess, Brooke Shipley, The homotopy theory of coalgebras over a comonad, Proc. London Math. Soc. (2014) 108 (2): 484-516.(arXiv:1205.3979)

This refers to the concept of “Postnikov presentation” of model categories due to appendix section 5 of

• Kathryn Hess, Homotopic Hopf-Galois extensions: foundations and examples, New topological contexts for Galois theory and algebraic geometry (BIRS 2008), Geom. Topol. Monogr., vol. 16, Geom. Topol. Publ., Coventry, 2009, pp. 79–132. MR 2544387 (2010j:55010) (arXiv:0902.3393)