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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan lie lie-theory 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 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 science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory 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 topiclinear logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 12
- Last comment by TobyBartels
- Last Active Feb 17th 2020

The cut rule for linear logic used to be stated as

If $\Gamma \vdash A$ and $A \vdash \Delta$, then $\Gamma \vdash \Delta$.

I don’t think this is general enough, so I corrected it to

If $\Gamma \vdash A, \Phi$ and $\Psi,A \vdash \Delta$, then $\Psi,\Gamma \vdash \Delta,\Phi$.

- Discussion Type
- discussion topic2-category
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Thomas Holder
- Last Active Feb 17th 2020

promted by demand from my Basic-Course-On-Category-Theory-Students I expanded the entry 2-category:

mentioned more relations to other concepts in the Idea-section;

added an Examples-section with a bunch of (classes of) examples;

added a list of references. Please add more if you can think of more!

- Discussion Type
- discussion topicCritique of Pure Reason
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 30
- Last comment by Thomas Holder
- Last Active Feb 16th 2020

I added a discussion of space in Kant’s Transcendental Aesthetics in Critique of Pure Reason.

By the way, the translation of the quote from Kant in the section “On Aristotelian logic” seem a bit strange: I think the original German sentence was “Begriffe aber beziehen sich als Prädikate möglicher Urtheile auf irgend einen noch unbestimmten Gegenstand” (“But conceptions, as predicates of possible judgements, relate to some representation of a yet undetermined object.”).

PS The automatic function to create this thread in the nforum did not word.

- Discussion Type
- discussion topiccohomotopy
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active Feb 16th 2020

At the old entry

*cohomotopy*used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.(We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

- Discussion Type
- discussion topicmean value theorem
- Category Latest Changes
- Started by TobyBartels
- Comments 9
- Last comment by TobyBartels
- Last Active Feb 15th 2020

Urs had earlier started mean value theorem with just a link to Wikipedia. I have now added content. Constructive versions to come, hopefully; for now, see this forum post.

- Discussion Type
- discussion topicjoin
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Feb 15th 2020

- Discussion Type
- discussion topickaon
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 15th 2020

starting a stub, for the moment just to record som references on potential flavour anomalies in kaon-decays:

- Andrzej J. Buras,
*The Revival of Kaon Flavour Physics*(arXiv:1609.05711)

- Andrzej J. Buras,

- Discussion Type
- discussion topicquantum error correction
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Feb 14th 2020

- Discussion Type
- discussion topiccategory of G-sets
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Feb 14th 2020

- Discussion Type
- discussion topicquantum chemistry
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Feb 14th 2020

added these pointers on application of tensor networks (specifically tree tensor networks) in quantum chemistry:

Naoki Nakatani, Garnet Kin-Lic Chan,

*Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm*, J. Chem. Phys. 138, 134113 (2013) (arXiv:1302.2298)Henrik R. Larsson,

*Computing vibrational eigenstates with tree tensor network states (TTNS)*, J. Chem. Phys. 151, 204102 (2019) (arXiv:1909.13831)

- Discussion Type
- discussion topicNadrian Seeman
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 14th 2020

brief

`category:people`

-entry for hyperlinking references at*quantum chemistry*

- Discussion Type
- discussion topicBoris Khesin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 14th 2020

brief

`category:people`

-entry for hyperlinking references at*hydrodynamics*

- Discussion Type
- discussion topichydrodynamics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 14th 2020

added pointer to today’s

- Benjamin Doyon,
*Lecture notes on Generalised Hydrodynamics*(arXiv:1912.08496)

- Benjamin Doyon,

- Discussion Type
- discussion topicknot
- Category Latest Changes
- Started by zskoda
- Comments 7
- Last comment by Urs
- Last Active Feb 14th 2020

I added the definition and several references on higher dimensional knots under knot.

- Discussion Type
- discussion topictopological quantum computation
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 14th 2020

added missing publication data to some references, and added this new reference:

- D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov,
*A modular functor which is universal for quantum computation*, Nucl. Phys. B926 (2018) 491-508 (arXiv:1703.00431)

- D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov,

- Discussion Type
- discussion topicquantum computation
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Feb 14th 2020

stub for

*quantum computation*

- Discussion Type
- discussion topicA Concise Course in Algebraic Topology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 14th 2020

- Discussion Type
- discussion topicMacNeille real number
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by TobyBartels
- Last Active Feb 14th 2020

The pages MacNeille real number and MacNeille completion disagree about whether $\pm\infty$ are MacNeille real numbers. The former says the MacNeille reals are the MacNeille completion of the rationals and hence contain $\pm\infty$, whereas the latter says that the MacNeille reals are obtained by “dropping $\pm\infty$” from that completion. Which should it be?

The Elephant also contains a definition of “MacNeille real number” that is more general than a Dedekind cut, but doesn’t contain $\pm\infty$: instead of “locatedness” (if $a\lt b$ are rationals then $a\in L$ or $b\in U$) they satisfy “if $a\lt b$ and $a\notin L$ then $b\in U$” and “if $a\lt b$ and $b\notin U$ then $a\in L$”. Since $L$ and $U$ are both required to be inhabited, this definition also excludes $\pm\infty$. But it’s not clear to me how it’s related to the general definition of MacNeille completion. It would be nice to include a comparison at the page MacNeille real number.

- Discussion Type
- discussion topicThe Multifaceted Skyrmion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 13th 2020

- Discussion Type
- discussion topicskyrmion
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Feb 13th 2020

- Discussion Type
- discussion topicIsmail Zahed
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 13th 2020

- Discussion Type
- discussion topicMannque Rho
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 13th 2020

- Discussion Type
- discussion topicCarlos Naya
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 13th 2020

- Discussion Type
- discussion topicneutron star
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 13th 2020

added pointer to discussion of models of neutron stars by Skyrmions:

- Carlos Naya,
*Neutron stars within the Skyrme model*, Int. J. Mod. Phys. E 28, 1930006 (2019) (arXiv:1910.01145)

- Carlos Naya,

- Discussion Type
- discussion topicStefano Bolognesi
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 13th 2020

brief

`category:people`

-entry for hyperlinking references at*Skyrmion*and at*AdS/QCD correspondence*

- Discussion Type
- discussion topicMarcus Tressl
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Feb 13th 2020

- Discussion Type
- discussion topicstar-autonomous category
- Category Latest Changes
- Started by Mike Shulman
- Comments 22
- Last comment by nLab edit announcer
- Last Active Feb 12th 2020

I added to star-autonomous category a mention of “$\ast$-autonomous functors”.

- Discussion Type
- discussion topicmodal homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Feb 12th 2020

copied over the homotopy-theoretic references from

*modal type theory*to here.

- Discussion Type
- discussion topicTaro Kimura
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 12th 2020

- Discussion Type
- discussion topicGilbert Ryle
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Feb 12th 2020