Not signed in (Sign In)

A discussion forum about contributions to the nLab wiki and related areas of mathematics, physics, and philosophy.

Want to take part in these discussions? Sign in if you have an account, or apply for one below

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundle bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

- 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 topicEk-Algebras
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active Dec 7th 2009

started extracting stuff from Ek-Algebras

added the statement of the main result and created a new subsection at k-tuply monoidal n-category to link to it

renamed the previous entry E-k operad into little cubes operad

- 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 topicbiactegory
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Nov 30th 2009

- I created biactegory following my 2006 work and being prompted by overlapping work of a student of Nikshych which appeared on the arXiv today.

- 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!