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 beauty bundles calculus categorical 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 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 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 homological homological-algebra 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 measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 topicrational Todd class is Chern character of Thom class
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

am giving this theorem its own little entry, for ease of cross-linking relevant other entries, such as

*Todd class*,*chern character*,*Thom class*

- Discussion Type
- discussion topicTodd class
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 5 days ago

added (here) statement that the e-invariant is Todd class of cobounding (U,fr)-manifolds

- Discussion Type
- discussion topicBoardman homomorphism
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 5 days ago

created some minimum at

*Boardman homomorphism*(the thing generalising the Hurewicz homomorphism)

- Discussion Type
- discussion topicAdams e-invariant
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by David_Corfield
- Last Active 5 days ago

added rough description and original citation to

*Adams e-invariant*

- Discussion Type
- discussion topicFRW model
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

some basics at

*FRW model*(in cosmology)

- Discussion Type
- discussion topiccharmonium
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicBekenstein-Hawking entropy
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

added pointer, here and in related entries, to

- Gary Gibbons, Malcolm J. Perry,
*Black Holes and Thermal Green Functions*, Vol. 358, No. 1695 (1978) (jstor:79482)

being one of the early references considering the computation of black hole radiation in terms of thermal field theory on Wick-rotated spacetimes with compact/periodic “Euclidean time”.

- Gary Gibbons, Malcolm J. Perry,

- Discussion Type
- discussion topicExt
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 6 days ago

tried to edit Ext a bit. But this needs to be expanded, eventually.

- Discussion Type
- discussion topiclong exact sequence in generalized homology
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicatomic geometric morphism
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active 6 days ago

started atomic geometric morphism

- Discussion Type
- discussion topicHeyting algebra
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Dmitri Pavlov
- Last Active 6 days ago

I tried to structure the entry Heyting algebra a bit more. Check if you like it.

I also added a little bit to the Examples-section.

In the section on toposes it says that a “Grothendieck (0,1)-topos” is a locale. Is that correct? Shouldn’t it say: a Grothendieck (0,1)-topos is a category of open subsets of a topological space?

- Discussion Type
- discussion topicprincipal bundle
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by zskoda
- Last Active 6 days ago

I have added to

*principal bundle*a remark on their

*definition*As quotients;statements about (classes of) (counter-)examples of quotients

Thanks for pointers to the literature from this MO thread!

- Discussion Type
- discussion topiclong exact sequence in homology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

a disambiguation page, for

- Discussion Type
- discussion topiclong exact sequence in chain homology
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 6 days ago

I am beginning to split off from

*fiber sequence*an entry*long exact sequence in homology*(also splitting off all the related redirects, such as long exact sequence in cohomology etc).

- Discussion Type
- discussion topicprojective structure
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 6 days ago

- Discussion Type
- discussion topicprojectively flat connection
- Category Latest Changes
- Started by Bartek
- Comments 2
- Last comment by zskoda
- Last Active 6 days ago

- Discussion Type
- discussion topichomotopical algebraic geometry
- Category Latest Changes
- Started by adeelkh
- Comments 2
- Last comment by David_Corfield
- Last Active 6 days ago

Started something at homotopical algebraic geometry, have to run now.

- Discussion Type
- discussion topicstable homotopy category
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Urs
- Last Active 6 days ago

That doesn’t look right at Via left homotopy of spectra. $\ell$ is supposed to be the forgetful functor from spectra to prespectra.

But what kind of spectra are we looking at? It seems to be coordinate-free spectrum. So then we need a definition of prespectrum.

- Discussion Type
- discussion topicfinite homotopy limits of spectra -- section
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

Earlier today I was checking where on the $n$Lab we had recorded basics on finite homotopy (co)limits of spectra. But it seems we haven’t at all, except for the discussion at

*Introduction to Stable homotopy theory*.So then I started to add something at

*Spectra*, only to notice that this needs harmonizing/merging with the parallel entry*stable (infinity,1)-category of spectra*.To cut this Gordian knot, I am now creating hereby an entry with a bare section on finite homotopy (co)limits of spectra, to be

`!include`

ed into these entries (and into*stable homotopy category*and maybe elsewhere, too).So far I have just some bare minimum here. Deserves to be expanded.

- Discussion Type
- discussion topicSpectrum
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicSpin(5)
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by DavidRoberts
- Last Active 7 days ago

- Discussion Type
- discussion topicHochschild cohomology
- Category Latest Changes
- Started by Urs
- Comments 100
- Last comment by Tim_Porter
- Last Active 7 days ago

I am in the process of preparing a piece on Hochschild cohomology

while the Lab is down, I'll abuse the forum here for posting my source. Probably not well suited for reading it, but just so the effort is not wasted should my notebook get run over by a bus. That could happen, as the buses here in Sheffield go on the wrong side of the road.

See followup comment...

- Discussion Type
- discussion topicSpin(6)
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicQuillen1967AHT-ref
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicpure morphism
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active 7 days ago

pure morphism (much more to be said, and more references, but no time now)

- Discussion Type
- discussion topicd-invariant
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 7 days ago

Just for completeness, to go with

*e-invariant*and*f-invariant*.

- Discussion Type
- discussion topicmodel structure for Cartesian fibrations
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Hurkyl
- Last Active Jan 14th 2021

renamed model structure on marked simplicial oversets to model structure for Cartesian fibrations

merged the material that was at marked simplicial set (now marked simplicial set > history) into this entry

expanded the entry a bit, but still working on it...

- Discussion Type
- discussion topicGrothendieck category
- Category Latest Changes
- Started by zskoda
- Comments 13
- Last comment by zskoda
- Last Active Jan 14th 2021

I strongly disagree with the statement in Grothendieck category that the Grothendieck category is small. The main examples like ${}_R Mod$ are not! What did the writer of that line have in mind ?

- Discussion Type
- discussion topicmathematics presented in homotopy type theory
- Category Latest Changes
- Started by David_Corfield
- Comments 31
- Last comment by Urs
- Last Active Jan 14th 2021

- Discussion Type
- discussion topictorus
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Jan 14th 2021

Added a subsection

### As a homotopy type

As a homotopy type the torus is the product of two copies of the circle.

In homotopy type theory the torus can be formalized as the higher inductive type generated by a point

`base`

, two paths, $p$ and $q$, from`base`

to itself, and an element $t$ of $p\cdot q = q \cdot p$. It has been formally shown (Sojakova15) that this type is equivalent to the product of two circles. For a treatment in cubical type theory, see (Licata-Brunierie).