nLab model structure on coalgebras over a comonad

Contents

Context

Model category theory

model category, model \infty -category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for equivariant \infty-groupoids

for rational \infty-groupoids

for rational equivariant \infty-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general \infty-algebras

specific \infty-algebras

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Contents

Idea

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

References

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

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)

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