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    • brief category:people-entry for hyperlinking references

      v1, current

    • Aleks Kissinger has contacted me about his aims to start a collection of nLab entries on quantum information from the point of view of the Bob Coecke school.

      Being very much delighted about this offer, I created a template entry quantum information for his convenience.

    • brief category:people-entry for hyperlinking references

      v1, current

    • I corrected an apparent typo:

      A 2-monad TT as above is lax-idempotent if and only if for any TT-algebra a:TAAa \colon T A \to A there is a 2-cell θ a:1ηa\theta_a \colon 1 \Rightarrow \eta \circ a

      to

      A 2-monad TT as above is lax-idempotent if and only if for any TT-algebra a:TAAa \colon T A \to A there is a 2-cell θ a:1η Aa\theta_a \colon 1 \Rightarrow \eta_A \circ a

      It might be nice to say η A\eta_A is the unit of the algebra….

      diff, v22, current

    • I’ve wondered for a while whether there is a notion of lax-idempotent 2-adjunction, but for some reason until now I’d never thought to try the obvious route of simply generalizing the conditions defining an idempotent adjunction. Haven’t had time to cross-link it yet.

    • I have created lax morphism, with general definitions and a list of examples. It would be great to have more examples.

    • starting page on type theories with parametricity, as a separate article from the article on polymorphism.

      Anonymouse

      v1, current

    • at monadicity theorem in the second formulation of the theorem, item 3, it said

      CC has

      I think it must be

      DD has

      and have changed it accordingly. But have a look.

    • A stub. Hopefully those more knowledgeable will add some content.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • reformatted the entry group a little, expanded the Examples-section a little and then pasted in the group-related “counterexamples” from counterexamples in algebra. Mainly to indicate how I think this latter entry should eventually be used to improve the entries that it refers to.

    • starting page on hierarchy of universes in type theory

      Anonymouse

      v1, current

    • I added a sentence to fundamental group which contains a link to an example for a fundamental group of an affine scheme.
    • I wrote out a proof which uses very little machinery at fundamental theorem of algebra. It is just about at the point where it is not only short and rigorous, but could be understood by an eighteenth-century mathematician. (Nothing important, just fun!)

    • I have created the entry recollement. Adjointness, cohesiveness etc. lovers should be interested.

    • a stub, for completeness and to have a place to record references

      v1, current

    • Long overdue entry. Though I am not aiming to do the topic justice here. While I wrote some lines of an Idea-section it’s a stub entry, for the time being just to record the numerical value of the magnetic flux quantum in various units.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a bit, including the original reference by G. B.

      diff, v7, current

    • “for each nonzero element rr in a semiprimitive ring,…module left annihilated by rr.” to “…module not left annihilated by rr.”

      Anonymous

      diff, v7, current

    • added a warning to the top of the page to alert the reader of the issue that some browsers may render the page in a meaningless way (as per discussion here)

      But I don’t think the slash notation is used much at all elsewhere on the nLab, so that there is not much to worry about here.

      diff, v5, current

    • I got tired of having to fight my way through Kelly’s monster yet again, and created transfinite construction of free algebras. I couldn’t really think of a good name for this page; suggestions are welcome.

    • Bare minimum containing a couple of definitions.

      v1, current

    • Added work on Ologs and started restructuring the page

      rTuyeras

      diff, v5, current

    • added to Kan lift the def of absolute Kan lifts, and some more examples.

      Btw, in all of the sources I’ve read about this, Kan lifts are simply called (left, right) liftings. What do you think about renaming this to liftings? will it conflict with some other kind of “lifting”?

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a “warning” for something that tripped me up: the classifying topos of a classical first-order theory is typically not Boolean, even though the classifying pretopos is Boolean. For a topos to be Boolean is much stronger – as Blass and Scedrov showed, it implies 0\aleph_0-categoricity.

      diff, v31, current

    • I am moving the following old query box exchange from orbifold to here.

      old query box discussion:


      I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely does not view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.

      Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?

      Urs Schreiber: please, go ahead. It would be appreciated.


      end of old query box discussion

    • starting page on universe as a disambiguation page

      v1, current

    • I noticed that there was a neglected stub entry universe that failed to link to the fairly detailed (though left in an unpolished state full of forgotten discussions) Grothendieck universe.

      I renamed the former to universe > history and made “universe” redirect to “Grothendieck universe”

    • I have checked with the WaybackMachine for when was the last time it succeeded in taking a snapshot of the “Manifold Atlas” (which is down and has been for a while).

      I have added my findings as a little paragraph to the entry:

      The site is down and has been for some time. The last successful snapshot made by the WaybackMachine is, for the landing page, from 2024, Dec 26 and, for the “bulletin” page, from 2025, Feb 28. The latest update to the latter dates back to 2017.

      So it does look likely that the site is gone for good.

      diff, v6, current

    • starting disambiguation page on multiverse

      v1, current

    • I kept being annoyed about the nature of discussion of the “multiverse” (the one in cosmology, not the one in set theory). Now I thought instead of steadily being annoyed, I should start an nnLab entry that does it better. So I did now (or tried to), at multiverse.

    • Since I was being asked I briefly expanded automorphism infinity-group by adding the internal version and the HoTT syntax.

      Mike, what’s the best type theory syntax for the definition of Aut(X)\mathbf{Aut}(X) via \infty-image factorization of the name of XX?

    • I rewrote a good bit of the entry sheaf, trying to polish and strengthen the exposition.

      The rewritten material is what now constituttes the section “Definition”. This subsumes essentially everything that was there before, except for some scattered remarks which I removed and instad provided hyperlinks for, since they have meanwhile better discussions in other entries.

      I left the discussion of sheaves and the general notion of localization untouched (it is now in the section “Sheaves” and localization”). This would now need to be harmonized notationally a bit better. Maybe later.

    • Move the text of the “Idea” section from the title to the body. Previously, the title contained the entire paragraph.

      SamoN

      diff, v22, current