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I started writing folk model structure on Cat with an explicit summary of the construction, and a description of how it can be modified to work if you assume only COSHEP. I feel like there should also be a "dual" model structure assuming some other weakening of choice, in which all categories are cofibrant and the fibrant objects are the "stacks", but I haven't yet been able to make it come out right.
Mike Shulman wrote weak factorization system on Set, which is very nice.
Motivated by this question on MO, created weak factorization system on Set and added some comments about size questions to anafunctor.
expanded the Idea-section at schreiber:oo-Lie differentiation and integration and polished the section of oo-Lie diffeentiation somewhat, following the blog discussion here
Discussion has spilt from the categories
mailing list into evil.
Sridhar Ramesh has one at Grothendieck fibration.
I started algebraic category, with a note also at monadic adjunction.
created infinity-limits - contents and added it as a toc to relevant entries
(maybe I shoulod have titled the page differently, but it doesn't matter much for a toc)
started expanding butterfly
also butterfly diagrams at crossed profunctor
filled a gap in deRham theorem for oo-Lie groupoids on my personal web.
But I need to sleep over this...
created a section Contractible objects at lined topos.
This introduces and discusses a bit a notion of objects being contractible with respect to a specified line object (maybe the section deserves to be at interval object instead, not sure).
This notion is something I made up, so review critically. I am open for suggestions of different terminology. The concept itself, simple as it is (though not entirely trivial), I need for the discussion of path oo-groupoids of oo-stacks on my personal web:
if a lined Grothendieck topos is such that all representable objects are contractible with respect to the line object , then the path oo-groupoid functor
on simplicial sheaves, which a priori is only a Qulillen functor of oo-prestacks, enhances to a Quillen functor of oo-stacks (i.e. respects the local weak equivalences).
An incomplete introduction to shape fibration and a related bio entry Sibe Mardesic.
Somebody wrote quite the stub at Beck-Chevalley_Condition; I fixed the name but didn't mess with it otherwise. It seems to have appeared (properly named) on Mike's web too, all by the AnonymousCoward.
Added to the Idea section at space and quantity a short paragraph with pointers to the (oo,1)-categorical realizations. (Parallel to the blog discussion here)
homeopathic definition at bar construction
no, I didn't create an entry with that title.
but I added to n-fibration a brief link, though, to the concept that is currently described at Cartesian fibration, which models Grothendieck fibrations of (oo,1)-categories.
This here is mainly to remind me that there is need to polish and reorganize the nLab entries on higher fibrations into something more coherent.
I fixed a bunch of broken links on the lab just now. In case anybody is wondering what all of those edits were.
Just look at the list of all wanted pages, here are a few stubby articles: 1-topos, 2-Hilbert space, Alexandroff compactification, Banach manifold. (Yes, I went alphabetically.)
I have just made links to all of the contentful orphaned paged on the main nLab web. However, they may still be walled gardens; Instiki doesn't find those automatically.
In general, when you create a new page, it's a good idea to create a link to it from some existing page on a more general topic. (The links that I just made may not have been the best!) That way, it's more likely that people will actually find their way to your new page.
I wanted to start expanding on the big story at nonabelian Lie algebra cohomology, but then found myself wanting to polish first a bit further the background material.
I came to think that it is about time to collect our stuff on "oo-Lie theory".
So I created a floating table of contents
and added it to most of the relevant entries.
This toc is based on the one on my personal web here -- but much larger now -- and still contains some links to my web, where I am trying to develop the full story. If anyone feels ill-at-ease with these links to my personal web, let me know.
I created Riemann surface and Myers-Steenrod theorem.
I started classical mathematics to link to from internal logic.
It looked to me like Urs hit Ctrl-V instead of Ctrl-C there, so I rolled back, but now Urs is editing again, so probably he's just doing something that I interrupted. Since I can't leave a note there now, I'll leave one here: I won't interfere again, Urs.
added to (infinity,1)-operad the definition/proposition of the model structure for the category of (oo,1)-categories of operations here
Or possibly not by Maarten. Anyway, there is some discussion at superdifferential form and Weil algebra that people into that sort of thing should look at.
I added to vertical categorification the comments that I'd made at MathOverflow, as Urs has requested. I'm not sure that I'm happy with where I put them and how I labelled them, but maybe it's better if other people judge that.
New item homotopy coinvariants functor, after a paper of Kathryn Hess. For now just a definition.
More discussion about this at category theory.
Gavin Wraith wrote geometric theory.
New entry Eckmann-Hilton duality. Discussion welcome.
Created universal algebra in a monoidal category
In the lab book metaphor, this page is some jottings of stuff that I'm pretty sure must be out there (as it's a fairly obvious thing to do) but have no idea of what it's called (hedgehogs, perhaps?). So I'd be grateful if someone strong in the ways of Lawvere theories could stop by and help me out.
(Plus I had to make up the notation and terminology as I went along so that's all horrible)
Hopefully the big box at the top of the page makes this clear!
One of these has started (or continued) a conversation at the bottom of graph.
I'm guessing that ferrim is spam. If no-one says anything to the contrary within 24hrs then I'll add it to the spam category.
If it is spam, it's either a random spambot post or it's someone testing to see how vigilant we are. If the latter, as there's no content then they may simply test to see if the link stays active. In which case, our previous "policy" of blanking the content won't send the right signal here (especially as there's no content to blank). Is there any objection to renaming spam entries? Say, as 'spam (original title)' (or whatever the allowable punctuation characters are)?
I asked a question at dendroidal set and wrote normal monomorphism to explain it.
added to symmetric monoidal smash product of spectra a link to a pdf with seminar notes that nicely recall the definition of the symmetric monoidal category of spectra.
In entry groupoid object in an (infinity,1)-category there is a passage
"it is the generalization of Stasheff H-space from Top to more general ?-stack (?,1)-topoi: an object that comes equipped with an associative and invertible monoid structure, up to coherent homotopy"
I repeat what I documented in earlier discussion on H-space: H-spaces are widely used terminology since 1950, thus before Stasheff work which of course is an important work on coherencies for them. So it is likely improper to say Stasheff H-space...Stasheff has REFINEMENTS of H-spaces, namely $A_n$-spaces and the group-like case is A infty spaces.
Somebody named ‘Harry’ has a comment at evil. Presumably it is of interest to Mike and me.
I see Mike's 1-category equipment
May I vote for the following: we should "play Bourbaki" and correct the naming mistake made here. The obvious name one should use is "pro-morphism structure".
We equip a category with pro-morphisms.
We equip a category with a pro-morphism structure.
Or, if you insist,
We equip a category with pro-arrows.
We equip a category with a pro-arrow structure.
But the day will come when you want a pro-2-morphism structure. And then one will regret having used "arrow" instead of "morphism".
I mean, compared to issues like "presentable" versus "locally presentable", this idea of saying just "equipment" is a bit drastic, to my mind.
I'd like to write something about a Quillen equivalence, if any, between model structures on
n-connected pointed spaces
grouplike E-n spaces .
With the equivalence given by forming n-fold look spaces.
But I need more input. I found a nice discussion of a model structure on n-connected pointed spaces in A closed model category on (n-1)-connected spaces. I suppose there is a standard model structure on E-k algebras in Top. Is a Quilen equivalence described anywhere?
Oh, and I copied over most of my exposition from the cafe post on equipments to 2-category equipped with proarrows.
Created small presheaf, and replaced the very old discussion at Grothendieck universe by a link to small presheaf.
Does anyone know any references that treat the case of small sheaves, in this sense?
I added to directed colimit the -directed version, for some regular cardinal .
We should maybe also add to directed set the -directed version. What we currently descrribe there is just the -directed version.
Accordingly then I also added to compact object the definition of the variant of -compact objects.
At small object previously it mentioned "-filtered colimits". I now made that read "-directed colimits".
I hope that's right. If not, do we need to beware of the differene?
created entry for Dan Freed and added some links to articles by him here and there
expanded the discussion of face maps at dendroidal set a little
I put a question at CommCoalg for those knowledgeable about accessible categories: is this category locally presentable?
I've almost completely redone algebraic category, following the Joy of Cats. I also briefly added quasivarieties to variety of algebras.
Query box at monoidal functor.
Added some discussion to skeletal category about how skeletality doesn't imply uniqueness-on-the-nose for categorical constructions, tempting though it may be to suppose that.
Somewhat stubby beginning, but with a link to an old paper of Barr which may turn out to be useful for universal algebra in a monoidal category. Some discussion of measuring coalgebras is generalized to the framework of PROPs.
I've started work at the zen garden (doriath). Stage one is to add customisable tags to all the pieces that we can reasonably adjust in the CSS. At the moment, these are all in red to make it easy to see them and to see if I've done it right - I ran it through a script to add tags to everything and I know that it got confused once or twice so there's a bit of manual work to do. Once I'm happy with that, I'll put up a sample along the lines of what Toby was thinking: having the CSS declarations in separate pages that can be "swapped in" with a minimum effort. Then people can copy that and see what the Zen Garden looks like with their changes. I'll try to make the sample so that it's really easy to change things so that those without and CSS knowledge can still have a go.
created shifted tangent bundle because I thought somebody was asking about that on the blog, but now looking more closely I find that maybe nobody asked for that...
… between David Roberts and me at ionad and Morita equivalence.
Etymology and pronunciation at ionad