Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

(0 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundle bundles calculus categories category category-theory chern-simons-theory chern-weil-theory cobordism cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent differential differential-cohomology differential-geometry duality education elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra general topology geometric-quantization geometry goodwillie-calculus gravity group-theory higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory hypercovers index-theory infinity integration-theory internal-categories k-theory kan lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure measure-theory modal-logic model model-category-theory monoidal monoidal-category monoidal-category-theory morphism motives motivic-cohomology newpage nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory phenomenology philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject supergeometry symplectic-geometry synthetic-differential-geometry terminology theory topological topology topos topos-theory tqft type type-theory

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeMay 18th 2012

    The preprint The homotopy theory of coalgebras over a comonad by Hess and Shipley looks interesting. Among other things it contains

    • a theorem about replacing a model structure by a Quillen equivalent one in which the cofibrations are the monomorphisms
    • a theorem about when the category of coalgebras for a comonad inherits a model structure by “left transfer”.

    I wonder whether there could be a model structure on coalgebraically cofibrant objects?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 18th 2012

    Ah, thanks for pointing this out. I had heard them speak about that, but didn’t see the article appear.

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 9th 2014

    The “left transfer” part is developed further in this paper:, which basically develops a theory dual to the usual theory of transferred model structures:

    Left-induced model structures and diagram categories

    Marzieh Bayeh, Kathryn Hess, Varvara Karpova, Magdalena Kedziorek, Emily Riehl, Brooke Shipley

    We prove existence results for and verify certain elementary properties of left-induced model structures, of which the injective model structure on a diagram category is an important example. We refine our existence results and prove additional properties for the injective model structure. To conclude, we investigate the fibrant generation of (generalized) Reedy categories. In passing, we also consider the cofibrant generation, cellular presentation, and small object argument for Reedy diagrams.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 9th 2014

    Thanks. I have added that citation now to the References-section at transferred model structure