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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 23rd 2012

added to generalized Reedy category a bunch of definitions and propositions from Cisinski’s article, concerning the notion of normal morphisms of presheaves over a generalized Reedy category.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeFeb 23rd 2012

Thanks! I just had a look at this page for the first time since Cisinski’s notion was added. I was a bit confused about which statements and examples were about which definition, so I tried to clarify; but please correct if I got it wrong.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeFeb 23rd 2012

Hi Mike,

yes, sorry, I had added this only today and then was interrupted before I had really cleaned up the expanded entry. I will expand further on this in more detail in the next days.

• CommentRowNumber4.
• CommentAuthorJonasFrey
• CommentTimeSep 24th 2019

I think there’s a little problem on this page: Cisinski’s “catégories squelettiques” are introduced as a generalization of Reedy categories, and are actually referred to as “Cisinski generalized Reedy categories”. However, I don’t think that they actually generalize Reedy categories: in a Cisinski category, all negative maps are split epis, but for Reedy categories arising from inverse categories this property only holds in trivial cases (when the inverse category is discrete).

To fix this, I think we have to start by changing terminology. What should we say instead of “Cisinski generalized Reedy category”? Maybe “Cisinski category”? Or “skeletic category”?

• CommentRowNumber5.
• CommentAuthorJonasFrey
• CommentTimeSep 24th 2019

Or maybe “Cisinski-skeletal category” in analogy to “Barr-exact”.

• CommentRowNumber6.
• CommentAuthorRichard Williamson
• CommentTimeSep 25th 2019
• (edited Sep 25th 2019)

I think ’skeletal category’ is good, can always be qualified with ’in the sense of Cisinki’ if necessary.

• CommentRowNumber7.
• CommentAuthorTodd_Trimble
• CommentTimeSep 26th 2019

I like Cisinski-skeletal.

• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeSep 26th 2019

skeletal category has a standard meaning, so any other usage of it should be qualified somehow. But since Cisinski’s categories are so much like Reedy categories, I think it would be good to name them accordingly, rather than perpetuating unnecessary confusion. Maybe “Cisinski-Reedy category”?