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- Discussion Type
- discussion topicfinite-rank complex orientation and MΩΩSUn -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 29th 2020

a bare list of references, to be

`!include`

-ed in pertinent stand-alone entries, such as at*complex oriented cohomology theory*and at*MΩΩSU(n)*

- Discussion Type
- discussion topicThom spectrum
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Urs
- Last Active Dec 29th 2020

wrote out parts of the proof of $\Omega^{un}_\bullet \simeq \pi_\bullet M O$ at Thom spectrum

- Discussion Type
- discussion topiccrossed module
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 10
- Last comment by Richard Williamson
- Last Active Dec 29th 2020

At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group $\pi_2(X,A)$ together with the bundary map $\delta:\pi_2(X,A)\to \pi_1(A)$ and the $\pi_1(A)$-action on $\pi_2(X,A)$. As someone confirms this example is correct I’ll add it to crossed module.

- Discussion Type
- discussion topicnull homotopy
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Dec 29th 2020

- Discussion Type
- discussion topicweakly reductive semigroup
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Dec 29th 2020

- Discussion Type
- discussion topicring
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Todd_Trimble
- Last Active Dec 28th 2020

at the beginning of

*ring*I have spelled out a more explicit definition. Also added the examples of rings on cyclic groups to explain the origin of the word “ring”.

- Discussion Type
- discussion topicdivergence theorem
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Dec 28th 2020

- Discussion Type
- discussion topicembedding tensor
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Dec 28th 2020

- Discussion Type
- discussion topicembedding tensors and tensor hierarchy in super Lie theory -- section
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 28th 2020

this is a bare sub-section, to be

`!include`

-ed into the pertinent entries (at*embedding tensor*, at*tensor hierarchy*and at*super Lie algebra*) in order to avoid having to copy this stuff around and to facilitate updating and syncing it across these entries

- Discussion Type
- discussion topictopos
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Dmitri Pavlov
- Last Active Dec 26th 2020

Added a table of contents to topos, a section on "special classes" and one on "higher toposes".

- Discussion Type
- discussion topiccartesian bicategory
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by Todd_Trimble
- Last Active Dec 26th 2020

Added the references

Aurelio Carboni, Bob Walters,

*Cartesian Bicategories, I*, articleAurelio Carboni, Max Kelly, Bob Walters, Richard Wood,

*Cartesian Bicategories II*, (arXiv:0708.1921)

- Discussion Type
- discussion topicJordan superalgebra
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Todd_Trimble
- Last Active Dec 26th 2020

- Discussion Type
- discussion topicmonad
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by nLab edit announcer
- Last Active Dec 25th 2020

following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.

Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.

- Discussion Type
- discussion topicKan simplicial manifold
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active Dec 24th 2020

Today I was asked for what I know about the development of the theory of Kan-fibrant simplicial manifolds. I realized that the nLab does not discuss this, so I have started a page now with the facts that come to mind right away. (Likely I forgot various things that should still be added.)

- Discussion Type
- discussion topicdinatural transformation
- Category Latest Changes
- Started by Mike Shulman
- Comments 7
- Last comment by Todd_Trimble
- Last Active Dec 24th 2020

Expanded dinatural transformation a little with examples and references.

- Discussion Type
- discussion topicsimplicial manifold
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Dmitri Pavlov
- Last Active Dec 24th 2020

created stub for simplicial manifold

- Discussion Type
- discussion topicMartin-Löf dependent type theory
- Category Latest Changes
- Started by Zhen Lin
- Comments 20
- Last comment by maxsnew
- Last Active Dec 24th 2020

I started an article about Martin-Löf dependent type theory. I hope there aren't any major mistakes!

One minor point: I overloaded $\mathrm{cases}$ by using it for both finite sum types and dependent sum types. Can anyone think of a better name for the operation for finite sum types?

- Discussion Type
- discussion topicSophie Morel
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Dec 24th 2020

- Discussion Type
- discussion topicadic space
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Dec 23rd 2020

- Discussion Type
- discussion topicpseudofunctor
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by John Baez
- Last Active Dec 23rd 2020

I added a section on strictification of pseudofunctors $C \to Cat$ to pseudofunctor, after seeing Finn and Mike respond to Karol in the stable monoidal derivator thread at the Café. The discussion is fairly sketchy and pedestrian. Also added a few references.

- Discussion Type
- discussion topicintegers object
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Dec 23rd 2020

- Discussion Type
- discussion topicBoone conjecture
- Category Latest Changes
- Started by Martti_Karvonen
- Comments 4
- Last comment by Martti_Karvonen
- Last Active Dec 23rd 2020

The conjecture is not true for all single-sorted algebraic theories and this was known by Soviet mathematicians. I added a short high-level explanation on this and some references to translated works that have more detail. Presumably one should edit rest of the page (and references to it) to make it clear throughout that (i) the conjecture is false (ii) the general question “Which algebraic categories have the Higman property?” is still interesting (and potentially something category-theorists could study).

- Discussion Type
- discussion topicLawvere theory
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by Martti_Karvonen
- Last Active Dec 23rd 2020

started a Properties-section at Lawvere theory with some basic propositions.

Would be thankful if some experts looked over this.

Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

- Discussion Type
- discussion topicHigman's embedding theorem
- Category Latest Changes
- Started by Martti_Karvonen
- Comments 1
- Last comment by Martti_Karvonen
- Last Active Dec 23rd 2020

- Discussion Type
- discussion topicalgebraically compact category
- Category Latest Changes
- Started by Sam Staton
- Comments 9
- Last comment by Urs
- Last Active Dec 23rd 2020

- Discussion Type
- discussion topictemporal logic
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by nLab edit announcer
- Last Active Dec 23rd 2020

I added a couple of references for the claim

There is a Curry–Howard correspondence between linear-time temporal logic (LTL) and functional reactive programming (FRP).

How about for CLT and CLT* (in the computation tree logic section)?

Were we looking to integrate this section with the one above on temporal type theory as an adjoint logic, could there be a way via some branching representation of our type $Time$ as a tree?

I see Joachim Kock has an interesting way of presenting trees.

- Discussion Type
- discussion topicexponential law for spaces
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Todd_Trimble
- Last Active Dec 23rd 2020

The induced map most likely isn’t a homeomorphism when $X, Y$ are locally compact Hausdorff.

The original statement was in monograph by Postnikov without proof.

Not only that, in the current form it couldn’t possibly be true, since the map could lack to be bijective.

For more details see here: https://math.stackexchange.com/questions/3934265/adjunction-of-pointed-maps-is-a-homeomorphism .

I’ve added a reference in the case when $X, Y$ are compact Hausdorff though.

Adam

- Discussion Type
- discussion topicPontryagin-Thom construction -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 23rd 2020

this is a bare list of references, to be

`!include`

-ed into relevant entries(various parts of this list have been contained at

*Cohomotopy*,*Cohomotopy charge map*,*Thom’s theorem*,*Pontryagin-Thom construction*and elsewhere; this here now to ease harmonizing/completing these lists)

- Discussion Type
- discussion topicAdam Keenan
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 23rd 2020

- Discussion Type
- discussion topicMladen Bestvina
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 23rd 2020