nLab
model structure on dg-comodules

Contents

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

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

A model category structure on the category of comodules in chain complexes over a dg-coalgebra.

Details

Let CC be a differential graded-cocommutative coalgebra over a field.

Model structure of the second kind

There exists a model category structure on the category CdgCoModC dgCoMod of dg-comodules over CC whose

This is due to (Positelski 11, 8.2 Theorem (a)).

Model structure of the first kind

There is another model structure where the fibrations in addition satisfy the condition that their kernel KK satisfies that for all acyclic NN, then Hom̲ C(N,K)\underline{Hom}_C(N,K) is acyclic.

This is due to (Positelski 11, 8.2 Remark), there called the “model category structure of the first kind”. This is also reviewed as (Pridham 13, prop. 2.2).

References

Last revised on June 6, 2017 at 12:22:12. See the history of this page for a list of all contributions to it.