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2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicthe logic S5(m)
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 21 minutes ago

- Discussion Type
- discussion topicequivariant Hopf degree theorem
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active 2 hours ago

am finally splitting this off from

*Hopf degree theorem*, to make the material easier to navigate. Still much room to improve this entry further (add an actual Idea-statement to the Idea-section, add more examples, etc.)

- Discussion Type
- discussion topicHermann Nicolai
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 hours ago

- Discussion Type
- discussion topicD=3 supergravity
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 hours ago

- Discussion Type
- discussion topicdark matter
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active 4 hours ago

stub for

*dark matter*

- Discussion Type
- discussion topicmodal type theory
- Category Latest Changes
- Started by Urs
- Comments 86
- Last comment by Urs
- Last Active 4 hours ago

created an entry

*modal type theory*; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with*monad (in computer science)*.

- Discussion Type
- discussion topictransfor
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by nLab edit announcer
- Last Active 20 hours ago

I moved (n,k)-transformation to transfor, as seemed to be agreed upon by those who spoke up in the discussion there.

- Discussion Type
- discussion topicKarol Borsuk
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 23 hours ago

- Discussion Type
- discussion topicabsolute retract
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 23 hours ago

splitting off this definition from

*neighborhood retract*, for ease of linking, and in order to record the characterization AR = ANR+contractible

- Discussion Type
- discussion topicenriched monad
- Category Latest Changes
- Started by Sam Staton
- Comments 8
- Last comment by David_Corfield
- Last Active 1 day ago

- Discussion Type
- discussion topicequivariant Tietze extension theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topiccountable set
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Mike Shulman
- Last Active 1 day ago

Somebody sent me an email with the following comment on the entry

*countable set*. I am not in position to react to this, maybe some expert here could reply. The sentence being quoted originates from revision 1 of the entry.Forwarded message:

“We do have, however, that a countable set is either empty or inhabited, which is classically trivial but need not hold constructively for every set.”

(https://ncatlab.org/nlab/show/countable+set)

The set D={n\in N | 2n+6 is not the sum of two odd primes} is decidable, hence countable. However we cannot decide whether it is empty or inhabited. (We could decide it if we assumed LPO, for instance.)

Do you agree?

- Discussion Type
- discussion topiccategorical compositional distributional semantics
- Category Latest Changes
- Started by julesh
- Comments 8
- Last comment by Mike Shulman
- Last Active 1 day ago

Created an article for DisCoCat (which is a major industry in the Oxford Quantum Group), plus an incoming link from linguistics

- Discussion Type
- discussion topicJan Jaworowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

brief

`category:people`

-entry for hyperlinking references at*cohomotopy*and at*equivariant Tietze extension theorem*

- Discussion Type
- discussion topicextension theorems -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topiccharacteristic
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicHaskell
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 1 day ago

- Discussion Type
- discussion topicorthogonal subcategory problem
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Sam Staton
- Last Active 1 day ago

Made a start on this at orthogonal subcategory problem. There should be much more to say about this with regard to various generalities in model category theory. Needs some clean-up. Please have a look.

- Discussion Type
- discussion topicsymmetric monoidal category
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by Richard Williamson
- Last Active 2 days ago

added to symmetric monoidal category a new Properties-section As models for connective spectra with remarks on the theorems by Thomason and Mandell.

- Discussion Type
- discussion topicfpqc topology
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicGraeme Segal
- Category Latest Changes
- Started by Andrew Stacey
- Comments 10
- Last comment by Urs
- Last Active 2 days ago

There has GOT to be a better photograph than that! Is there anyone here in Oxford? Can they go and get a picture for us?

- Discussion Type
- discussion topicproof assistant
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by atmacen
- Last Active 2 days ago

this MO comment made me realize that we didn’t have an entry

*proof assistant*, so I started one

- Discussion Type
- discussion topictoo simple to be simple
- Category Latest Changes
- Started by Oscar_Cunningham
- Comments 33
- Last comment by nLab edit announcer
- Last Active 3 days ago

(Hi, I’m new)

I added some examples relating too simple to be simple to the idea of unbiased definitions. The point is that we often define things to be simple whenever they are not a non-trivial (co)product of two objects, and we can extend this definition to cover the “to simple to be simple case” by removing the word “two”. The trivial object is often the

*empty*(co)product. If we had been using an unbiased definition we would have automatically covered this case from the beginning.I also noticed that the page about the empty space referred to the naive definition of connectedness as being

“a space is connected if it cannot be partitioned into disjoint nonempty open subsets”

but this misses out the word “two” and so is accidentally giving the sophisticated definition! I’ve now corrected it to make it wrong (as it were).

- Discussion Type
- discussion topicweak enrichment
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 5 days ago

- Discussion Type
- discussion topiccodensity monad
- Category Latest Changes
- Started by Thomas Holder
- Comments 6
- Last comment by Sam Staton
- Last Active 5 days ago

- Discussion Type
- discussion topicholographic entanglement entropy
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 5 days ago

created a stub for

*holographic entanglement entropy*in reaction to this MO question.

- Discussion Type
- discussion topicAdS-QCD correspondence
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicstrong monad
- Category Latest Changes
- Started by Sam Staton
- Comments 4
- Last comment by Sam Staton
- Last Active 6 days ago

- Discussion Type
- discussion topicactegory
- Category Latest Changes
- Started by maxsnew
- Comments 8
- Last comment by Sam Staton
- Last Active 6 days ago

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

stub for

*toric variety*