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 bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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 subobject 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 topicsmooth loci
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Oct 8th 2009

created stub for smooth loci

(should it be "smooth locus" instead?)

- Discussion Type
- discussion topicgeneralized smooth algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 7th 2009

sty addition to generalized smooth algebra: remark on terminology added and section on "internal definition" added.

planning to polish thinmgs later

- Discussion Type
- discussion topicIsrael Gelfand
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 7th 2009

created entry on Israel Gelfand with the material that John posted to the blog.

turns out the "Timeline" entry was already requesting it

- Discussion Type
- discussion topicmicrolinear space
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by TobyBartels
- Last Active Oct 6th 2009

created microlinear space

One thing I might be mixed up above:

in the literature I have seen it seems to say that

$ X^D x_X X^D \simeq X^{D(2)}$

with

$ D(2) = { (x_1,x_2) \in R \times R | x_i x_j = 0} $.

But shouldn't it be

$ D(2)' = { (x_1,x_2) \in R \times R | x_i^2 = 0} $.

?

- Discussion Type
- discussion topicsynthetic differential geometry - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 6th 2009

started synthetic differential geometry - contents and added it as floating table of contents to the relevant entries

- Discussion Type
- discussion topicinfinitesimal space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 6th 2009

quick addition of "formal infinitesimal spaces" and Weil algebras to infinitesimal space

but am planning to polish this entry further later, it is a bit of a mess at the moment

- Discussion Type
- discussion topicintegration axiom
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 6th 2009

started integration axiom, but incomplete for the moment

at schreiber:integration of oo-Lie algebroid valued differential forms I am thinking about the higher version of this

- Discussion Type
- discussion topiccyclic things
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by David_Corfield
- Last Active Oct 5th 2009

Looks like maybe Todd is right at cyclic order that the cycle category cannot be defined in that way.

- Discussion Type
- discussion topicAdded detexify to online resources
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Oct 5th 2009

Just learnt about detexify from the Secret Blogging Seminar and thought it worth adding to the online resources page.

- Discussion Type
- discussion topicNew pages
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Oct 5th 2009

- Discussion Type
- discussion topicnatural isomorphism
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 4th 2009

A little more detail at natural isomorphism, including when one can speak of the functor satisfying certain conditions.

- Discussion Type
- discussion topicsynthetic differential geometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 4th 2009

I worked on synthetic differential geometry:

I rearranged slightly and then expanded the "Idea" section, trying to give a more comprehensive discussion and more links to related entries. Also added more (and briefly commented) references. Much more about references can probably be said, I have only a vague idea of the "prehistory" of the subject, before it became enshrined in the textbooks by Kock, Lavendhomme and Moerdijk-Reyes.

Also, does anyone have an electronic copy of that famous 1967 lecture by Lawvere on "categorical dynamics"? It would be nice to have an entry on that, as it seems to be a most visionary and influential text. If I understand right it gave birth to topos theory, to synthetic differential geometry and all that just as a spin-off of a more ambitious program to formalize physics. If I am not mistaken, we are currently at a point where finally also that last bit is finding a full implmenetation as a research program.

- Discussion Type
- discussion topicsmooth topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 4th 2009

created smooth topos on the axioms on toposes used in synthetic differential geometry.

- Discussion Type
- discussion topichonoring Dubuc's work on synthetic differential geometry
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 4th 2009

By chance I came across an old CatTheory mailing list post by e. Dubuc, where he complains about how is work on SDG is not sufficiently recognized and asks people to speak of the "Dubuc topos".

I added a remark about this to synthetic differential geometry in the section on "Well adapted models".

- Discussion Type
- discussion topicI found another term for a [[tight relation]].
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by TobyBartels
- Last Active Oct 4th 2009

I found another term for a tight relation.

- Discussion Type
- discussion topicon moduli stack of elliptic curves
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 1st 2009

A few more sections at A Survey of Elliptic Cohomology - elliptic curves on

topol. invariants of the moduli stack of ell. curves

the compactified version

the definition of Gromov-Witten invariants

an example.

As before, this is raw material which I am thinking lends itself to be turned into entries.

- Discussion Type
- discussion topicsynthetic differential supergeometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 1st 2009

started synthetic differential supergeometry

so far just to record the (three!) references

- Discussion Type
- discussion topicpeople entries. D'Auria, Fre, Castellani, Sati
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 1st 2009

created entries for the following people

Riccardo D'Auria, Pietro Fre, Leonardo Castellani, Hisham Sati

not much there, yet, but these pages serve a purpose as listing the pages that link to them, which is useful I think

- Discussion Type
- discussion topicgroup object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 1st 2009

Added to group object the Yoneda-embedding-style definition and added supergroup to the list of examples.

- Discussion Type
- discussion topicsupergroup
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 1st 2009

Added the Yoneda-embedding way to talk about group objects and hence supergroups.

- Discussion Type
- discussion topicInstructions
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Oct 1st 2009

A list of all recently edited entries can be seen at Recently Revised. But that list tends to contain lots of minor changes: it's not easy to spot the important ones. So, if you feel people's attention should be drawn to some changes you make, then please mention them

*here*. This way the rest of us can spot them, so we can learn what you know — and maybe make further improvements!- Go to the Latest Changes category in the Forum. If you are reading this on the forum, then you are there right now, or go to http://www.math.ntnu.no/~stacey/Vanilla/nForum/?CategoryID=5.
- Optionally, create an account (if you don't have one) and log in if necessary; this may be helpful but is not required.
- Hit ‘Start new discussion’ at the upper left.
- Choose a meaningful subject title, perhaps the name of the page you've edited or something like that.
- Write a brief message summarising your edit. Most of the formatting is the same as on the Lab if you choose the ‘Markdown+Itex’ radio button beneath the comment box.
- Please include a
`[[wikilink]]`

to the page or pages that you edited. - If you didn't log in, then please also include your name.
- Check Preview Post (or skip it), and then Start your discussion!

Questions? Ask them here!

- Discussion Type
- discussion topicString Lie 2-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 30th 2009

created String Lie 2-algebra

- Discussion Type
- discussion topicexterior differential system
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 30th 2009

uploaded course notes by Bryant to exterior differential system (linked to from the Reference section)

- Discussion Type
- discussion topicblob homology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 30th 2009

Added references to blob homology.

- Discussion Type
- discussion topicArchives
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Sep 30th 2009

Here are archives of the changes before 2009 October:

- 2009 September
- 2009 August
- 2009 July
- 2009 June
- 2009 May
- 2009 April
- 2009 March
- 2009 February
- 2009 January
- 2008

See also all changes.