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2 added 235 characters in body

Hello,

This probably just technical, but anyway:

In "Simplicial Homotopy Theory" by Goerss and Jardine, chap. III, par. 2, after cor. 2.12, they describe a model structure on $Ch^{+}$, the category of chain complexes in non-negative degress. Equivalences are quasi-isom., fibrations are those maps which are surjective in degrees $n \ge 1$ (notice the $1$!).

Then they note: "After the fact, it turns out that the cofibrations are those monomorphisms of chain complexes having degreewise projective cokernels".

It seems this is not correct as stated. Maybe if it would say $n \ge 0$ upstairs it would be correct, but we do have $n \ge 1$ (corresponding to the picture of simplicial abelian groups).

Is it a typo or I don't understand something? Is there a nice description of cofibrations in this case?

Thank you, Sasha

Update: I was just confused with homological/cohmological indexing conventions. One needs either chains in positive degrees, or cochains in negative degrees. I by mistake used positive degrees as they, but with cochains - by habit.

1

Hello,

This probably just technical, but anyway:

In "Simplicial Homotopy Theory" by Goerss and Jardine, chap. III, par. 2, after cor. 2.12, they describe a model structure on $Ch^{+}$, the category of chain complexes in non-negative degress. Equivalences are quasi-isom., fibrations are those maps which are surjective in degrees $n \ge 1$ (notice the $1$!).

Then they note: "After the fact, it turns out that the cofibrations are those monomorphisms of chain complexes having degreewise projective cokernels".

It seems this is not correct as stated. Maybe if it would say $n \ge 0$ upstairs it would be correct, but we do have $n \ge 1$ (corresponding to the picture of simplicial abelian groups).

Is it a typo or I don't understand something? Is there a nice description of cofibrations in this case?

Thank you, Sasha