# Start a new discussion

## Not signed in

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

## Discussion Tag Cloud

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

• CommentRowNumber1.
• CommentAuthorZhen Lin
• CommentTimeAug 6th 2013

I added two characterisations of weak homotopy equivalences to model structure on simplicial sets.

For the record, I found the inductive characterisation in Cisinski’s book [Les préfaisceaux comme modèles des types d’homotopie, Corollaire 2.1.20], but I feel like I’ve seen something like it elsewhere. The characterisation in terms of internal homs comes from Joyal and Tierney [Notes on simplicial homotopy theory], but they take it as a definition.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 27th 2021
• (edited Jul 27th 2021)

I have added full publication data and section-pointers to a bunch of the references we had here, and cleaned up the list a little (slight re-organization, slight tweaking of wordings, for streamlining). For instance, it seemed to make no sense to list the proof by Goerss&Jardine not among the list including those by Gelfand&Manin and by Joyal&Tierney.

Then I added those further references we had at classical model structure on simplicial sets but not here yet.

In fact it’s a pain that I should go now to do the same updating there. So this means that instead I should make this references-section a stand-alone entry to be !include-ed here and there. Will do this now at:

classical model structure on simplicial sets – references

1. Reference pointed to the wrong section of Goerss-Jardine.

Anonymous