Contents

model category

for ∞-groupoids

# Contents

## Idea

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

## Details

Let $C$ be a differential graded-cocommutative coalgebra over a field.

Model structure of the second kind

There exists a model category structure on the category $C dgCoMod$ of dg-comodules over $C$ 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 $K$ satisfies that for all acyclic $N$, then $\underline{Hom}_C(N,K)$ 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.