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I have started an entry on the decalage functor.
Thanks!
Your link to homotopy n-type made me edit that entry a little: I removed John Baez's query box asking what a "homotopy type" is, and instead added a very first sentence to the entry intended to make the connection with the entry homotopy type clear.
I fixed a typo.
Might I suggest 'truncated' rather than 'coarsened' which is a term I tend to avoid? Just as one might extract a fundamental group (1-type) from a homotopy type one can try to extract a model for the 2-type, etc. with difficulties of course as this will be up to equivalence. I think of the n-type as encoding a certain amount of (more usable) information about the homotopy type of the object, and `coarsened' suggests a different relationship. I seem to remember that the entry does make the point about the use of the term to mean a homotopy type having no non-trivial info above dimension n, which is another valuable insight.
I added two references which in memory are relevant (somebody could look into to check my reasoning).
Sure, "truncated" is better.
I have added two other early uses of the idea, Illusie and Duskin. (I need to check out Duskin as there are some neat facts about augmented simplicial sets and decalage in it. I have a version in the notes but must see what might go in the Lab entry.)
Good I was going to do just that and to mention how augmented simplicial sets were ... and I forget what! I was going to look it up.
Todd, you forgot to sign it!!
That was not quite what I was going to do. I was going to describe the TOTAL dec functor and then its link with ordinal sum. (I should do that!)
Todd, it seems to me like your last edits appeared signed with the user name "Anonymous Coward". That's the default user name that appears when you don't enter one.
When you hit "submit" on any entry, there is a field where you can enter your name, as I am sure you know.
You probably changed computers and the new one doesn't have the cookie yet that remembers your nLab name.
I have added a brief mention of Total Decalage. This will need a new entry later on.
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