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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeJul 6th 2010

The entry test category which I wrote some time ago, came into the attention of Georges Maltsiniotis who kindly wrote me an email with a kind praise on nlab and noting that his Astérisque treatise on the topic of Grothendieck’s homotopy theory is available online on his web page and that the Cisinski’s volume is sort of a continuation of his Astérisque 301. Georges also suggested that we should emphasise that a big part of the Pursuing Stacks is devoted to the usage of test categories, so I included it into the bibliography and introductory sentence. I hinted to Georges that when unhappy with a state of an nlab entry he could just feel free to edit directly.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 17th 2011

I have added a Properties-section to test category, added more references and, mainly, added comments to the References, indicated what happens where and who did what. Please check.

Also created model structure on presheaves over a test category.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeSep 17th 2011
• (edited Sep 17th 2011)

added a brief remark to the Examples-section that also the groupoidal $\Theta$ is a test category

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeSep 18th 2011

There are few new typographic errors there: both Cisinkis and Cisinksi appear there, in addition to Cisinski.

• CommentRowNumber5.
• CommentAuthorTodd_Trimble
• CommentTimeSep 18th 2011

Zoran, I recall that you once expressed general annoyance about someone editing a page you had worked on (or were interested in) only to correct a spelling mistake or a grammar mistake – that it would cost you time (I guess a few seconds) to go in and find out that a recent change had been so minor.

I don’t recall which nForum thread that was in, so I no longer know whether you had recommended a course of action for dealing with this. I for one would like to be able to correct minor errors on pages, but in recent times I have resisted impulses to do this, to avoid having someone (like you) be irritated with me. (And yet, I see lots of discussion on things like whether we should write Pontryagin or Pontrjagin, an issue I couldn’t care less about, really, except for the fact that apparently I now have to remember to use a ’j’, against my former habit, if I want to avoid irritating anyone.)

I’ve now gotten tired of resisting urges to fix small errors, like spelling mistakes, because I believe lots of little mistakes have a cumulative negative effect. What would you have people do in this case – alert the nForum when such small revisions are made, explaining the nature of the revision? Is that what you would do?

I personally think a better and more sensible informal rule would be to leave notes about revisions at the nForum only when the reviser thinks it is important enough to merit attention, and just have people not to get too upset if one or two spelling mistakes are corrected without posting a notice. What do you think?

• CommentRowNumber6.
• CommentAuthorTodd_Trimble
• CommentTimeSep 19th 2011

(Rereading my comment #5, it might have come off as much more aggressive than I want it to, in which case I apologize. Still… I consider this an important issue.)

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeSep 19th 2011

By all means, please, if you have the energy, correct the mistakes, or, if you have not, alert me of it and make me do it.

I’ve fixed the ones on test category that I saw.

• CommentRowNumber8.
• CommentAuthorzskoda
• CommentTimeSep 19th 2011
• (edited Sep 19th 2011)

I think that no reporting on $n$Forum is needed for most minor edits. If somebody is currently working on a page is likely to work more, to generate new versions anyway, and I find it better that they receive the comments they about the subject and the entry they are currently interested in, then asking for those who notice to think how to incorporate their remarks. This is especially true when it is about the content. Say I see that the definition is similar but different to the one in reference I recall. The person who currently works on the entry will be interested in hearing about the difference and anyway invests time in clearing the concept out. For intervening in an entry in a subject I am currently not interested in, it would take me more than to write an entire entry n the subject I currently think. Well, this is obvious.

• CommentRowNumber9.
• CommentAuthorZhen Lin
• CommentTimeJul 18th 2013

I added the definition of strict test category, which was previously referred to in the examples section but not defined.

• CommentRowNumber10.
• CommentAuthorMatanP
• CommentTimeJul 19th 2013

Added the example of the tree category $\Omega$. I don’t have an access to the proof but I know Moerdijk gave a talk about it in the conference for the retirement of Georges Maltsiniotis, held in Paris about a month ago.

• CommentRowNumber11.
• CommentAuthorDmitri Pavlov
• CommentTimeMar 18th 2019

Added redirects for “weak test category” and “Grothendieck homotopy theory”.

• CommentRowNumber12.
• CommentAuthorTim Campion
• CommentTimeDec 20th 2019

The definition of “weak test category was incorrect”. Should be fixed now.

• CommentRowNumber13.
• CommentAuthorDmitri Pavlov
• CommentTimeDec 20th 2019
• (edited Dec 20th 2019)
The previous definition is actually equivalent to the new one
by Proposition 4.1.10(iv) in Cisinski,
which says that i^*_A(C) is aspherical for any C with a terminal object
if and only if the counit i_A i^*_A(C) → C is a (Thomason weak) equivalence of categories for all C.
• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeFeb 9th 2021

I have tried to streamline the sentence in the Idea-section a little. Also added more cross-links (such as with cellular set).