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- Discussion Type
- discussion topicRiemann surfaces and Myers-Steenrod theorem
- Category Latest Changes
- Started by amathew
- Comments 3
- Last comment by amathew
- Last Active Dec 15th 2009

I created [[Riemann surface]] and [[Myers-Steenrod theorem]].

- Discussion Type
- discussion topicNew page: [[classical mathematics]]
- Category Latest Changes
- Started by TobyBartels
- Comments 27
- Last comment by Urs
- Last Active Dec 15th 2009

I started classical mathematics to link to from internal logic.

- Discussion Type
- discussion topicframed bicategory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Dec 13th 2009

created quick stub for framed bicategory

but my machine's battery will die any second now...

- Discussion Type
- discussion topicEdit conflict at [[model structure on dendroidal sets]]
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by TobyBartels
- Last Active Dec 11th 2009

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.

- Discussion Type
- discussion topic(oo,1)-operads
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Dec 11th 2009

added to (infinity,1)-operad the definition/proposition of the model structure for the category of (oo,1)-categories of operations here

- Discussion Type
- discussion topicObjections by Maarten
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Urs
- Last Active Dec 10th 2009

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.

- Discussion Type
- discussion topicCategorification vs laxification
- Category Latest Changes
- Started by TobyBartels
- Comments 20
- Last comment by TobyBartels
- Last Active Dec 10th 2009

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.

- Discussion Type
- discussion topichomotopy coinvariants
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Dec 10th 2009

New item homotopy coinvariants functor, after a paper of Kathryn Hess. For now just a definition.

- Discussion Type
- discussion topicPresenting categories with large simplicial sets
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Harry Gindi
- Last Active Dec 10th 2009

More discussion about this at category theory.

- Discussion Type
- discussion topicGavin Wraith wrote [[geometric theory]].
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Dec 9th 2009

Gavin Wraith wrote geometric theory.

- Discussion Type
- discussion topicEvil composition
- Category Latest Changes
- Started by Harry Gindi
- Comments 2
- Last comment by Andrew Stacey
- Last Active Dec 9th 2009

- Discussion Type
- discussion topicTypes of shapes of limit cones
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 5
- Last comment by TobyBartels
- Last Active Dec 9th 2009

- I'd like to add the following "shape" to http://ncatlab.org/nlab/show/limit#types_of_shapes_of_limit_cones_17 :

The limit of the identity functor Id: C --> C is the initial object of C (it it exists).

- Discussion Type
- discussion topicPersonal web updated
- Category Latest Changes
- Started by Guest
- Comments 7
- Last comment by Guest
- Last Active Dec 9th 2009

- I've added the latest, almost complete, draft of my thesis to my personal web - go via David Roberts. Comments on introduction are welcome, if you feel so inclined. Just put them on David Roberts.

On a related note, is it quite legitimate to post updates on personal webs here? (Now that I've already done it)

David Roberts

- Discussion Type
- discussion topicEckmann-Hilton duality
- Category Latest Changes
- Started by zskoda
- Comments 11
- Last comment by zskoda
- Last Active Dec 8th 2009

New entry Eckmann-Hilton duality. Discussion welcome.

- Discussion Type
- discussion topicCategory theory
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by TobyBartels
- Last Active Dec 7th 2009

- Edited the page category theory. Mostly about that certain presheaves are the same as categories and the long discussion at the end with an idea how to solve my problem about CW-complexes. Removed precursors link since there is nothing about them in nLab. This new logging is a bit confusing and harder to read.

-Rafael

- Discussion Type
- discussion topicuniversal algebra in a monoidal category
- Category Latest Changes
- Started by Andrew Stacey
- Comments 35
- Last comment by Andrew Stacey
- Last Active Dec 7th 2009

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!

- Discussion Type
- discussion topicdouble bicategory
- Category Latest Changes
- Started by John Baez
- Comments 5
- Last comment by John Baez
- Last Active Dec 7th 2009

- I started a little page called double bicategory.

- Discussion Type
- discussion topicDefinition of extended TQFT
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 6
- Last comment by domenico_fiorenza
- Last Active Dec 5th 2009

- I apologize in case this discussion is already open and I have been unable to find it.

There is something I am unable to undrstand in the definition of extended TQFT as on the nLab page http://ncatlab.org/nlab/show/extended+topological+quantum+field+theory

Namely, it seems to me that the recursive definition should rather end with "smooth compact oriented (n-m+1)-manifolds to R-linear (m?2)-categories"

- Discussion Type
- discussion topicLong time lurker, first time writer
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Dec 5th 2009

One of these has started (or continued) a conversation at the bottom of graph.

- Discussion Type
- discussion topicferrim
- Category Latest Changes
- Started by Andrew Stacey
- Comments 9
- Last comment by Andrew Stacey
- Last Active Dec 4th 2009

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)?

- Discussion Type
- discussion topicNormal monomorphisms between dendroidal sets.
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Dec 4th 2009

I asked a question at dendroidal set and wrote normal monomorphism to explain it.

- Discussion Type
- discussion topicsymmetric spectra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 4th 2009

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.

- Discussion Type
- discussion topicH-space
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Dec 4th 2009

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.

- Discussion Type
- discussion topicAnonymous question
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Dec 4th 2009

Somebody named ‘Harry’ has a comment at evil. Presumably it is of interest to Mike and me.

- Discussion Type
- discussion topiccube
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Dec 4th 2009

- Added topological cube to cube, and removed some JA-esque redirects from terms like succubi and so forth.

David Roberts

- Discussion Type
- discussion topic1-category equipment
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by TobyBartels
- Last Active Dec 4th 2009

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.

- Discussion Type
- discussion topicn-connected spaces and E-n spaces
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 3rd 2009

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?

- Discussion Type
- discussion topicequipment
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Dec 2nd 2009

Oh, and I copied over most of my exposition from the cafe post on equipments to 2-category equipped with proarrows.

- Discussion Type
- discussion topicsmall presheaves
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Dec 2nd 2009

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?

- Discussion Type
- discussion topicdirected colimit
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by zskoda
- Last Active Nov 30th 2009

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?

- Discussion Type
- discussion topicthis and that
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 30th 2009

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

- Discussion Type
- discussion topicDold-Kan correspondence
- Category Latest Changes
- Started by John Baez
- Comments 2
- Last comment by Urs
- Last Active Nov 29th 2009

- I did a wee bit of editing of "Dold-Kan correspondence", trying to incorporate Kathryn Hess' wisdom into this page. A lot of this stuff involves the monoidal aspects of the Dold-Kan correspondence, but I was too lazy to edit the separate page "monoidal Dold-Kan correspondence". I would ideally like that page to focus equal attention to chain complexes as it now does to cochain complexes!

- Discussion Type
- discussion topicquestion at [[CommCoalg]]
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Todd_Trimble
- Last Active Nov 29th 2009

I put a question at CommCoalg for those knowledgeable about accessible categories: is this category locally presentable?

- Discussion Type
- discussion topicMore on algebraic categories
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 28th 2009

I've almost completely redone algebraic category, following the Joy of Cats. I also briefly added quasivarieties to variety of algebras.

- Discussion Type
- discussion topicAm I the only one who doesn't like the term 'comonoidal functor'?
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 28th 2009

Query box at monoidal functor.

- Discussion Type
- discussion topicskeletality and uniqueness
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Nov 25th 2009

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.

- Discussion Type
- discussion topic[[category of cocommutative coalgebras]]
- Category Latest Changes
- Started by Todd_Trimble
- Comments 23
- Last comment by Mike Shulman
- Last Active Nov 25th 2009

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.

- Discussion Type
- discussion topicBousfield localization of triangulated categories
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Nov 25th 2009

I split the material so far at "Bousfield localization" into

and made Bousfield localization itself a dismbiguation page.

Then I edited Bousfield localization of triangulated categories a bit and added some references.

I expect it should be true that the (left) Bousfield localization of a model category whose homotopy category is a triangulated category corresponds to the Bousfield localization of that triangulated homotopy category, but I don't discuss a statement to that extent yet.

I'd be grateful for explicit pointers to the literature on this. I haven't had time yet to look much even at the literature that I do list as BLoc for triang cats. Am too busy at the moment with BLoc for mod cats.

- Discussion Type
- discussion topicZen Garden
- Category Latest Changes
- Started by Andrew Stacey
- Comments 29
- Last comment by TobyBartels
- Last Active Nov 24th 2009

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.

- Discussion Type
- discussion topicshifted tangent bundle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Nov 24th 2009

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...

- Discussion Type
- discussion topicConversations …
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 24th 2009

… between David Roberts and me at ionad and Morita equivalence.

- Discussion Type
- discussion topicEtymology and pronunciation for ‘ionad’
- Category Latest Changes
- Started by TobyBartels
- Comments 9
- Last comment by TobyBartels
- Last Active Nov 23rd 2009

Etymology and pronunciation at ionad

- Discussion Type
- discussion topiclocal object
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 23rd 2009

Fixed/clarified the notation in the definition of local objects in a model category. Added references.

Also added references to (infinity,1)-categorical hom-space in that context.

- Discussion Type
- discussion topicGreg Egan's Euclidean geometry
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 22nd 2009

Following TWF 283, Greg Egan has created pentagon decagon hexagon identity (and Euclidean geometry to link to it), with several nice SVG pictures too.

- Discussion Type
- discussion topiccohomology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Nov 20th 2009

wrote a fairly long Idea section at cohomology

since the question keeps coming up and I noticed that the entry did a rather suboptimal job of describing the nice observation to be described here.

- Discussion Type
- discussion topicQuery at [[2-pullback]]
- Category Latest Changes
- Started by TobyBartels
- Comments 12
- Last comment by zskoda
- Last Active Nov 20th 2009

Zoran has already reported a query at 2-pullback, but I think that it should have wider exposure. I attempted a response.

- Discussion Type
- discussion topicFull iamge
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Nov 20th 2009

- Discussion Type
- discussion topicCategory theory vs order theory
- Category Latest Changes
- Started by TobyBartels
- Comments 53
- Last comment by TobyBartels
- Last Active Nov 20th 2009

I've been thinking about a pedagogical problem, so now I've written something about it at category theory vs order theory. Comments and examples welcome!

- Discussion Type
- discussion topicTwo new articles
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 20th 2009

- dual equivalence, pretty stubby, to take links that don't like they really want to go to either duality or opposite category
- full image, not so stubby

- Discussion Type
- discussion topicnegative thinking
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 19th 2009

added to negative thinking an explicit list of related entries and the floating higher cat theory toc

I think this is important enough to show the reader as much of the grand picture as possible

- Discussion Type
- discussion topicNew article: TAC
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Urs
- Last Active Nov 19th 2009

I figured that we could stand to have an article on

*TAC*, so I started one.

- Discussion Type
- discussion topicGelfand-Neumark
- Category Latest Changes
- Started by David_Corfield
- Comments 14
- Last comment by zskoda
- Last Active Nov 19th 2009

- I thought I'd add something about the Gelfand-Neumark theorem

The category of commutative von Neumann algebras is contravariantly equivalent to the category of localizable measurable spaces.

to measurable space, but see we don't have anything on localizability.

I also mentioned the theorem at von Neumann algebra. But what should one then say that a general von Neumann algebra is a noncommutative localizable measurable space? Normally one says noncommutative measure space.

- Discussion Type
- discussion topicRequest for references at commutative algebraic theory
- Category Latest Changes
- Started by Andrew Stacey
- Comments 4
- Last comment by Andrew Stacey
- Last Active Nov 18th 2009

The stuff at commutative algebraic theory is very interesting and I'd like to know some references! *looks at Todd, Toby, and Gavin*

- Discussion Type
- discussion topicDanger Todd Trimble!
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Todd_Trimble
- Last Active Nov 18th 2009

I may have overlapped an edit with you at initial algebra. ( It's no longer locked, but you didn't change it again, so maybe it timed out.)

- Discussion Type
- discussion topicmodel structure on simplicial presheaves and related
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Mike Shulman
- Last Active Nov 18th 2009

Over on MO Denis-Charles Cisinki kindly replied to some issues that I am recently working on here. See this.

- Discussion Type
- discussion topicCograph
- Category Latest Changes
- Started by Eric
- Comments 45
- Last comment by Eric
- Last Active Nov 17th 2009

It's not technically part of the main nLab (yet), but I asked a question at

- Discussion Type
- discussion topicdouble nerve
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 17th 2009

created stub entry for double nerve in reply to this MO question.

- Discussion Type
- discussion topicmodel structure on homotopical presheaves
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2009

started model structure on homotopical presheaves, where I collect the information that Denis-Charles Cisinski kindly provided here

I created a section "higher oo-stacks" at infinity-stack with a sentence about and a link to that.

- Discussion Type
- discussion topicn-symplectic manifold
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 17th 2009

created n-symplectic manifold

- Discussion Type
- discussion topicionads
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Nov 17th 2009

- Couple of points (pun not intended) at ionad. Also remark about categorified subobject classifiers

David Roberts