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- Discussion Type
- discussion topicsplit idempotent
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Feb 3rd 2019

I have added to the entry

*split idempotent*the statement (here) that in a triangulated category in which the direct sum of two triangles is a triangle, then idempotents split.(Maybe that should rather go into the entry

*Cauchy complete category*?)

- Discussion Type
- discussion topicJorge Santos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 3rd 2019

brief

`category:people`

-entry for hyperlinking references at*cosmic censorship hypothesis*and*weak gravity conjecture*

- Discussion Type
- discussion topiccosmic censorship hypothesis
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 3rd 2019

I have added to

*cosmic censorship hypothesis*pointer to the recent result (Crisford-Santos 17) showing that it is violated not just in higher dimensions, but also in four spacetime dimensions. And added a minimum of text to go with this. Also cross-linked with*weak gravity conjecture*.

- Discussion Type
- discussion topicrough paths
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Feb 3rd 2019

- Discussion Type
- discussion topicRR-field tadpole cancellation
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Feb 3rd 2019

started some bare minimum omn RR-field tadpole cancellation. Currently I am using this just to complement discussion at

*intersecting D-brane models*

- Discussion Type
- discussion topiccategory of cubes
- Category Latest Changes
- Started by Tim Campion
- Comments 1
- Last comment by Tim Campion
- Last Active Feb 3rd 2019

- Discussion Type
- discussion topichigher parallel transport
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Alizter
- Last Active Feb 3rd 2019

added pointer to

- Arthur Parzygnat,
*Two-dimensional algebra in lattice gauge theory*(arXiv:1802.01139)

which provides a wealth of computational details and illustrative graphics.

- Arthur Parzygnat,

- Discussion Type
- discussion topictensor network
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 3rd 2019

The term “tensor network”, while essentially just a synonym for “string diagram”, has in recent years become widely used and now fully established in quantum physics, especially in its use for discussion of

*holographic entanglement entropy*. It needs a page of its own, if only to point to*string diagram*while also listing the relevant physics references

- Discussion Type
- discussion topiccharacter of a linear representation
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Feb 3rd 2019

- Discussion Type
- discussion topicprefix order
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by Tim_Porter
- Last Active Feb 3rd 2019

I decided that nLab is probably a better place to develop my ideas than ‘wikipedia’, where I posted one article on this topic but never felt confident to add more, since wikipedia is not really meant for ’ongoing research’. I really liked the idea of using this space for ’public notes on my research’ and am looking forward to getting reactions from some of you.

As a starter, I feel that using the first-person form in my reporting is more ’honest’ regarding the academic status of the piece. Prefix orders are not an accepted notion in literature yet, I think. The notion itself is used often, but always in a specific context and was (as far as I know) never generalized - until now…

Pieter Cuijpers

- Discussion Type
- discussion topicadjoint functor
- Category Latest Changes
- Started by Urs
- Comments 44
- Last comment by Richard Williamson
- Last Active Feb 2nd 2019

added at adjoint functor

more details in the section In terms of universal arrows;

a bit in the section Examples

- Discussion Type
- discussion topicHowTo
- Category Latest Changes
- Started by Urs
- Comments 36
- Last comment by Richard Williamson
- Last Active Feb 2nd 2019

Have added to HowTo a description for how to label equations

In the course of this I restructured the section “How to make links to subsections of a page” by giving it a few descriptively-titled subsections.

- Discussion Type
- discussion topicmodel structure on cubical sets
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Richard Williamson
- Last Active Feb 2nd 2019

In the past we had some discussion here about why simplicial methods find so much more attention than cubical methods in higher category theory. The reply (as far as I am concerned at least) has been: because the homotopy theory = weak oo-groupoid theory happens to be well developed for simplicial sets and not so well developed for cubical sets. Historically this apparently goes back to the disappointment that the standard cubical geometric realization to Top does not behave as nicely as the one on simplicial sets does.

Still, it should be useful to have as much cubical homotopy theory around as possible. Many structures are more naturally cubical than simplicial.

So as soon as the Lab comes up again (we are working on it...) I want to create a page model structure on cubical sets and record for instance this reference here:

Jardine, Cubical homotopy theory: a beginning

- Discussion Type
- discussion topicPieter Cuijpers
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Pieter
- Last Active Feb 2nd 2019

- Discussion Type
- discussion topicmodel structure for quasi-categories
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by nLab edit announcer
- Last Active Feb 1st 2019

added some basics to

*model structure for quasi-categories*at*general properties*

- Discussion Type
- discussion topictree
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Richard Williamson
- Last Active Feb 1st 2019

- Discussion Type
- discussion topicmonadic functor
- Category Latest Changes
- Started by Alec Rhea
- Comments 4
- Last comment by Alec Rhea
- Last Active Jan 31st 2019

The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.

- Discussion Type
- discussion topicHigher Topos Theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jan 31st 2019

- Discussion Type
- discussion topicD(-2)-brane
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 31st 2019

- Discussion Type
- discussion topicANITA experiment
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 31st 2019

started some minimum, prodded by the suggestion in today’s replacement

- Bhavesh Chauhan, Subhendra Mohanty,
*A common leptoquark solution of flavor and ANITA anomalies*(arXiv:1812.00919)

that leptoquarks could not only explain the flavour anomalies but also the anomalous events seen last year by the ANITA experiment

- Bhavesh Chauhan, Subhendra Mohanty,

- Discussion Type
- discussion topicFernando Marchesano
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 31st 2019

brief

`category:people`

-entry for hyperlinking references at

- Discussion Type
- discussion topictable of marks
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Jan 31st 2019

- Discussion Type
- discussion topicVolodymyr Lyubashenko
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 31st 2019

- Discussion Type
- discussion topicintersecting D-brane model
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jan 30th 2019

**Edit to**: intersecting D-brane model by Urs Schreiber at 2018-04-01 00:55:01 UTC.**Author comments**:hyperlinked pointer to textbook by Ibanez-Uranga

- Discussion Type
- discussion topicFukaya category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 30th 2019

added pointer to section 7.5 of

- Fernando Marchesano,
*Intersecting D-brane Models*(arXiv:hep-th/0307252)

- Fernando Marchesano,

- Discussion Type
- discussion topicvon Neumann algebra factor
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active Jan 30th 2019

stub for von Neumann algebra factor

- Discussion Type
- discussion topicproper model category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Jan 30th 2019

I expanded proper model category a bit.

In particular I added statement and (simple) proof that in a left proper model category pushouts along cofibrations out of cofibrants are homotopy pushouts. This is at Proper model category -- properties

On page 9 here Clark Barwick supposedly proves the stronger statement that pushouts along all cofibrations in a left proper model category are homotopy pushouts, but for the time being I am failing to follow his proof.

(??)

- Discussion Type
- discussion topicGrp
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Urs
- Last Active Jan 30th 2019

- Discussion Type
- discussion topiccodense functor
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by David_Corfield
- Last Active Jan 30th 2019

- Discussion Type
- discussion topicslant product
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Jan 29th 2019