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- Discussion Type
- discussion topichomotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 66
- Last comment by Urs
- Last Active Nov 6th 2023

stub for homotopy type theory

- Discussion Type
- discussion topicGrpd
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2023

added pointer to:

- Erik Palmgren,
*Groupoids and local cartesian closure*(2003) [ pdf]

- Erik Palmgren,

- Discussion Type
- discussion topicJean Thierry-Mieg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2023

- Discussion Type
- discussion topicPeter D. Jarvis
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2023

- Discussion Type
- discussion topicKalb-Ramond field
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Nov 6th 2023

expanded and polished Kalb-Ramond field. In particular I added more references.

- Discussion Type
- discussion topicMuhammad Shafique
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2023

- Discussion Type
- discussion topicAlberto Marchisio
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2023

- Discussion Type
- discussion topiccanonical model structure on groupoids
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 5th 2023

- Discussion Type
- discussion topicfusion category
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by perezl.alonso
- Last Active Nov 5th 2023

briefly added something to fusion category. See also this blog comment.

- Discussion Type
- discussion topiclimit of a function
- Category Latest Changes
- Started by TobyBartels
- Comments 11
- Last comment by Urs
- Last Active Nov 5th 2023

- Discussion Type
- discussion topicpunctured neighborhood
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Nov 5th 2023

- Discussion Type
- discussion topicmodel structure on functors
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Nov 5th 2023

expanded model structure on functors by adding a long list of properties

- Discussion Type
- discussion topictest category
- Category Latest Changes
- Started by zskoda
- Comments 15
- Last comment by Hurkyl
- Last Active Nov 5th 2023

The entry test category which I wrote some time ago, came into the attention of Georges Maltsiniotis who kindly wrote me an email with a kind praise on nlab and noting that his Astérisque treatise on the topic of Grothendieck’s homotopy theory is available online on his web page and that the Cisinski’s volume is sort of a continuation of his Astérisque 301. Georges also suggested that we should emphasise that a big part of the Pursuing Stacks is devoted to the usage of test categories, so I included it into the bibliography and introductory sentence. I hinted to Georges that when unhappy with a state of an nlab entry he could just feel free to edit directly.

- Discussion Type
- discussion topicmonadic cohomology
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by Urs
- Last Active Nov 5th 2023

- Discussion Type
- discussion topicspin chain
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Nov 5th 2023

- Discussion Type
- discussion topicPolyakov gauge-string duality -- references
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 5th 2023

this is a bare subsection with a list of references, meant to be

`!include`

-ed into the References-lists of relevant entries (such as*AdS-QCD correspondence*,*AdS-QCD correspondence*but also at*flux tube*and maybe at*string*)

- Discussion Type
- discussion topicAlexei Morozov
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 5th 2023

- Discussion Type
- discussion topicdependent extension type
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by nLab edit announcer
- Last Active Nov 5th 2023

moving content on dependent extension types from type theory with shapes to its own page here

- Discussion Type
- discussion topictype universe
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Nov 5th 2023

I have created an entry type of types. Wanted to collect some literature there, but ended up not finding too much…

- Discussion Type
- discussion topicquadratic function
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by risingtides
- Last Active Nov 4th 2023

- Discussion Type
- discussion topichomogeneous function
- Category Latest Changes
- Started by risingtides
- Comments 1
- Last comment by risingtides
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicTomoyuki Arakawa
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicspecial geometry
- Category Latest Changes
- Started by perezl.alonso
- Comments 9
- Last comment by zskoda
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicbrane bouquet
- Category Latest Changes
- Started by perezl.alonso
- Comments 2
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicGromov-Witten invariants
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by perezl.alonso
- Last Active Nov 4th 2023

added pointer to:

- Albrecht Bertram,
*Stable Maps and Gromov-Witten Invariants*, School and Conference on Intersection Theory and Moduli Trieste, 9-27 September 2002 (pdf)

- Albrecht Bertram,

- Discussion Type
- discussion topicLöb's theorem
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicincompleteness theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 4th 2023

added publication details for:

- Russell O’Connor,
*Essential Incompleteness of Arithmetic Verified by Coq*, in:*Theorem Proving in Higher Order Logics. TPHOLs 2005*, Lecture Notes in Computer Science**3603**, Springer (2005) 245-260 [web, arXiv:cs/0505034, doi:10.1007/11541868_16]

- Russell O’Connor,

- Discussion Type
- discussion topicChu construction
- Category Latest Changes
- Started by Mike Shulman
- Comments 25
- Last comment by Todd_Trimble
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicCat
- Category Latest Changes
- Started by Peter Heinig
- Comments 17
- Last comment by Urs
- Last Active Nov 4th 2023

you can define $\Cat$ to be the 2-category of all $U'$-small categories, where $U'$ is some Grothendieck universe containing $U$. That way, you have $\Set \in \Cat$ without contradiction.

Do you agree with changing this to

” you can define $\Cat$ to be the 2-category of all $U'$-small categories, where $U'$ is some Grothendieck universe containing $U$. That way, for every small category $J$, you have the category $\Set^J$ an object of $\Cat$ without contradiction. This way, e.g. the diagram in Cat used in this definition of comma categories is defined. “

?

Reason: motivation is to have the pullback-definition of a comma category in (For others, it’s about the diagram here) defined, or rather, having Cat provide a way to make it precise. Currently, the diagrammatic definition can either be read formally, as a device to encode the usual definition of comma categories, or a reader can try to consult Cat in order to make it precise. Then they will first find only the usual definition of Cat having small objects only, which does not take care of the large category

$Set^I$

used in the pullback-definition. Then perhaps they will read all the way up to Grothendieck universes, but find that option not quite sufficient either since it only mentions Set, but not $Set^{Interval}$ . It seems to me that large small-presheaf-categories such as $Set^{Interval}$ can be accomodated, too, though.

(Incidentally, tried to find a “canonical” thread for the article “Cat”, by using the search, but to no avail. Therefore started this one.)

- Discussion Type
- discussion topiccolimit
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 7
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicWieslaw Pawlowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicAndrzej M. Borzyszkowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicMarek A. Bednarczyk
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topiccongruence
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Nov 4th 2023

touched the formatting in

*congruence*, fixed a typo on the cartesian square, added a basic example

- Discussion Type
- discussion topicIntroduction to Homotopy Theory
- Category Latest Changes
- Started by Oscar_Cunningham
- Comments 6
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topiccondensed mathematics
- Category Latest Changes
- Started by David_Corfield
- Comments 33
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicNathanael Arkor
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 4th 2023

- Discussion Type
- discussion topicHessian manifold
- Category Latest Changes
- Started by perezl.alonso
- Comments 1
- Last comment by perezl.alonso
- Last Active Nov 3rd 2023

definition to link to special geometry

- Discussion Type
- discussion topicweak wreath
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by varkor
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicdominant functor
- Category Latest Changes
- Started by varkor
- Comments 7
- Last comment by varkor
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicmonad retromorphism
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicretrofunctor
- Category Latest Changes
- Started by BryceClarke
- Comments 9
- Last comment by varkor
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicMax Kelly
- Category Latest Changes
- Started by varkor
- Comments 6
- Last comment by Urs
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topiccondensed local contractibility
- Category Latest Changes
- Started by David_Corfield
- Comments 91
- Last comment by Urs
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicHuan's inertia orbifold
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicTate K-theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Nov 3rd 2023

am finally splitting this off from

*Tate curve*

- Discussion Type
- discussion topictessarines
- Category Latest Changes
- Started by perezl.alonso
- Comments 2
- Last comment by Urs
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicsplit quaternion
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicsplit-complex numbers
- Category Latest Changes
- Started by perezl.alonso
- Comments 2
- Last comment by Urs
- Last Active Nov 3rd 2023

- Discussion Type
- discussion topicYoneda embedding
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Mark John Hopkins
- Last Active Nov 3rd 2023

Added Eric’s illustrations to the Idea-section at Yoneda embedding.

- Discussion Type
- discussion topicrepresentable functor theorem
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 8
- Last comment by Todd_Trimble
- Last Active Nov 3rd 2023

Added:

Specifically, a continuous functor $C\to Set$ is a right adjoint functor if and only if it is representable, in which case the left adjoint functor $Set\to C$ sends the singleton set to the representing object

## Related concepts

- Discussion Type
- discussion topiccomposition algebra
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by perezl.alonso
- Last Active Nov 2nd 2023

added pointer to today’s article by Ross Street:

A general abstract formulation of Rost 96 in terms of string diagrams in additive braided monoidal categories is in

- Ross Street,
*Vector product and composition algebras in braided monoidal additive categories*(arXiv:1812.04143)

- Ross Street,

- Discussion Type
- discussion topicpara-Hermitian manifold
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by perezl.alonso
- Last Active Nov 2nd 2023

- Discussion Type
- discussion topiccanonical model structure on Cat
- Category Latest Changes
- Started by Zhen Lin
- Comments 28
- Last comment by Urs
- Last Active Nov 2nd 2023

I added the remark that the canonical model structure on Cat is the model structure obtained by transferring the projective model structure on bisimplicial sets.

- Discussion Type
- discussion topiccanonical model structure
- Category Latest Changes
- Started by Richard Williamson
- Comments 3
- Last comment by Urs
- Last Active Nov 2nd 2023

Linking to the page canonical model structure for 2-categories in a couple of places.

- Discussion Type
- discussion topicEudoxus real number
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by varkor
- Last Active Nov 2nd 2023

Wrote an article Eudoxus real number, a concept due to Schanuel.

- Discussion Type
- discussion topicCoulomb branch
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by zskoda
- Last Active Nov 2nd 2023

- Discussion Type
- discussion topicnonabelian Stokes theorem
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Nov 2nd 2023

a little remark at

*nonabelian Stokes theorem*, still to be expanded

- Discussion Type
- discussion topicAGT correspondence
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active Nov 2nd 2023

I have expanded the Idea-section at

*AGT correspondence*, saying more explicitly how this may be thought of as regarding the 6d (2,0)-theory as a “2d SCFT with values in 4d SYM theories” and added pointers to further references (including some reviews).I have similarly expanded/added brief remarks on AGT/generalized S-duality pointing to this at

*6d (2,0)-SCFT – Compactification on Riemann surface*and at*S-duality – for SYM – From compactification*

- Discussion Type
- discussion topicclass S
- Category Latest Changes
- Started by zskoda
- Comments 6
- Last comment by zskoda
- Last Active Nov 2nd 2023