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Created semi-simplicial set, mainly as a repository for some terminological remarks. I would welcome anyone more knowledgeable about the history to correct or improve it!
Rourke and Sanderson looked at Delta sets. See the Wikipedia entry: http://en.wikipedia.org/wiki/Delta_set
I have added some references.
Various other weakened versions of simplicial set have been used, e.g., by Inassaridze.
This article appears to be blank, even though it has a nontrivial history.
This seems to be a recurring problem. Can we simply rerender all pages so that the problem goes away once and for all?
Richard kept saying that he kept doing just this, but that somehow it wasn’t so straightforward, due to remaining quirks.
Besides entries not displaying at all, I also keep running into entries whose tables, if any, appear with all items empty, until the page is being re-rendered.
Another problem is that special characters in people’s names got largely broken at some point (replaced by questions marks, mostly) thus also breaking links to these people’s entries, if any. This, too, needs people to look out for it and fix it.
I am hoping that eventually we’ll just catch all these pages by hand.
Just a slight clarification that I attempted re-rendering everything several times, but the attempts did not succeed for various technical reasons. This was somewhat early on during the period of rendering changes; there was significant progress later when I moved from using Maruku within Ruby on Rails to calling it externally, as a command line application. I could try re-rendering everything again now, but am reluctant, because there are still some small issues, and until those are fixed I think it best to just fix errant pages by hand (it seems now that several regulars recognise a problematic page when they see it and know how to re-render it).
The small issues should be solved by removing Maruku completely. This is what I intend to do next, but have not had any time to work on it for a number of weeks, and may not have time for some time to come, unfortunately.
The special characters issue predates my involvement, although I made matters partially worse I think at some point, back in the spring. There is no simple fix I know of for this; at some point I might be able to think of something, but it will never be 100% rigorous I think. These definitely should just be fixed as one sees them, as you suggest.
I could try re-rendering everything again now, but am reluctant, because there are still some small issues, and until those are fixed I think it best to just fix errant pages by hand (it seems now that several regulars recognise a problematic page when they see it and know how to re-render it).
Yes, absolutely.
How do you feel about creating new entries now with, potentially, special characters in the title, or even just using these special characters in links, via redirects to these entries. Is this safe now, or likely to break in the future as an unintended side effect of somebody working on the code?
Special characters should be absolutely fine now for all purposes (titles, links, page creations…). If you come across a bug, just let me know.
The original (or maybe not quite original) problem came from a one off search and replace which I believe (it was before I was involved) fixed what it was intended to fix, but had some side effects. My own attempts to improve the situation were of the same one off kind, with one off side effects. In hindsight we should not have replaced, but programatically made an edit, so that we could have rolled back/done a diff.
added a new section “Properties – Adjunction with simplicial sets” (here), stating the adjoint triple and the behaviour of weak homotopy equivalences under it.
For the statement that the unit of the left pair is a weak equivalence I pointed to Remark 5.8 in Rourke & Sanderson 71. That remark, however, just considers an unspecified inclusion, not making explicit that the unit map is meant. It must be, but it’s still awkward as a citation.
The article says:
There is a model structure on semi-simplicial sets, transferred along the right adjoint to the forgetful functor from the model structure on simplicial sets.
Is the forgetful functor a Quillen equivalence with respect to these model structures?
I haven’t looked into this at all, but at model structure on semi-simplicial sets we have a warning pointing to this comment by Karol Szumilo.
The discussion in the link does seem to answer the question in the affirmative. I wonder if there is a more stable reference for this.
I have searched a little but don’t find anything on the actual model structure. But, for what it’s worth, I have found discussion of various weaker structures (semi-model-, weak model-, (co)fibration-structure); which I have added here.
Added references to
Andrew Ranicki, Algebraic L-Theory and Topological Manifolds, Cambridge University Press 2002.
Thorsten Altenkirch, Paolo Capriotti, Nicolai Kraus, Extending Homotopy Type Theory with Strict Equality, CSL 2016, arXiv
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