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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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?)

• Created rough paths page. Need to add much more, and add some more pages about probability.

Anonymous

• Added a few additional descriptions of $\Box_{\leq 1}$, which is the same as $\Delta_{\leq 1}$.

• added pointer to

which provides a wealth of computational details and illustrative graphics.

• 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

• I am splitting this off from character (it used to just redirect there).

Currently I am just blindly moving the relevant material from there to here. That material is not great at all, and hopefully somebody eventually finds the energy to make a better entry.

• 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

• 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.

• 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:

• Page created, but author did not leave any comments.

• When writing my page on prefix orders, I found the need to refer to the page on trees. As it turns out, the order theoretic definition that I know for trees was not on it yet, so I decided to add it.

Pieter Cuijpers

• 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.

• Added link to the “current” version from Lurie’s web site, which is even more recently updated than the arXiv one.

• Page created, but author did not leave any comments.

• 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

• brief category:people-entry for hyperlinking references at

• started some minimum

• cross-linked with all $n$Lab pages that cite Lyubashenko

• Edit to: intersecting D-brane model by Urs Schreiber at 2018-04-01 00:55:01 UTC.

hyperlinked pointer to textbook by Ibanez-Uranga

• added pointer to section 7.5 of

• 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.

(??)

• Made a remark, to fill in a gap in the constructive proof that group monomorphisms are regular.

• Added a stub of an Idea section.

• Added a description of slant products in cohomology. Added references to Dold’s book.