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    • Fix a seemingly incorrect remark about the constructive case (together with minor edits). See https://math.stackexchange.com/questions/5085280/constructive-subtleties-about-the-sierpinski-space/5085447

      Trebor

      diff, v22, current

    • at subobject classifier I have cleaned up the statement of the definition and then indicated the proof that in locally small categories subobject classifiers precisely represent the subobject-presheaf.

    • Trivial edit: add the helping verb ’do’.

      TrivialEditor

      diff, v5, current

    • Trivial edit: change \colo to \colon.

      TrivialEditor

      diff, v22, current

    • I filled in a bit on the Wightman axioms. I also have a query there about adding an "axiom" environment to the LaTeX/CSS style sheets of nLab. I don't know how to do it on nLab but an axiom environment seems like it might be useful.
    • How would people feel about renaming distributor to profunctor? I seem to recall that when this came up on the Cafe, I was the main proponent of the former over the latter, and I've since changed my mind.

    • I made a little addition to opposite category, pointing out some amusing nuances regarding the opposite of a V-enriched category when V is merely braided. This remark could surely be clarified, but I think you’ll get the idea.

      (In case you’re wondering why I did this, it’s because I needed a reference for “opposite category” in a blog entry I’m writing.)

    • added English translation of this bit

      PN§260 Der Raum ist in sich selbst der Widerspruch des gleichgültigen Auseinanderseins und der unterschiedlosen Kontinuität, die reine Negativität seiner selbst und das Übergehen zunächst in die Zeit. Ebenso ist die Zeit, da deren in Eins zusammengehaltene entgegengesetzte Momente sich unmittelbar aufheben, das unmittelbare Zusammenfallen in die Indifferenz, in das ununterschiedene Außereinander oder den Raum.

      Space is in itself the contradiction of the indifferent being-apart and of the difference-less continuity, the pure negativity of itself and the transformation, first of all, to time. In the same manner time – since its opposite moments, held together in unity, immeditely sublate themselves – is the undifferentiated being-apart or: space.

      And polished a little around and following this bit.

      diff, v269, current

    • In the category:people-entry “William Lawvere” I have created a subsection “Motivation from foundations of physics” where I want to collect pointers to where and how Lawvere was/is motivated from finding foundations for (classical continuum) physics.

      Explicit evidence for this that I am aware of includes notably the texts Toposes of laws of motion and the introduction to the book Categories in Continuum Physics.

      The Wikipedia entry has this about motivation from physics:

      Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell. He learned of category theory [...] found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll. [...] meeting on “Categories in Continuum Physics” in 1982. Clifford Truesdell participated in that meeting, as did several other researchers in the rational foundations of continuum physics and in the synthetic differential geometry which had evolved from the spatial part of Lawvere’s categorical dynamics program). Lawvere continues to work on his 50-year quest for a rigorous flexible base for physical ideas, free of unnecessary analytic complications.

      Question: Can anyone point me to more on this early phase of the story (graduate student is supposed to start to look into continuum mechanics, starts to wonder “What is a vector field, really?, what a differential equation?” and ends up revolutionizing the foundations of differential calculus)?

    • I just aadded a sentence about Yang-Mills theory to gauge group, but there are some aspects of that article I feel we might want to discuss:

      I don’t think that the statement “gauge groups encoded redundancies” of the mathematical description of the physics is correct. One hears this every now and then, and I suppose the idea is the observation that physical observables have to be in the trivial representation of the gauge group, but there is more to the gauge group than that.

      Notably Yang-Mills theory is a theory of connections on G-principal bundles. No mathematician would ever say that the group G in a G-principal bundle just encodes a redundancy of our descriptins of that bundle. And the reason is because it is true only locally: the thing is that BG={*gG*} has a single object and hence is connected , but it has higher homotopy groups, and that’s where all the important information encoded by the gauge group sits.

      So I would say that instead of being a redundancy of the description, instead the gauge group of Yang-Mills theory enocedes precisely the homotopy type of its moduli space. This is rather important.

      A different matter are global gauge symmetries such as those that the DHR-theory deals with.

    • For now creating page, it needs to be (much) further expanded.

      v1, current

    • following discussion here, this is a page with a bare section, to be !include-ed into relevant entries (at wallpaper group, where it serves as illustration and at G-CW complex where it serves as examples)

      It’s not hard or surprising to produce these equivariant cell decompositions of the 2-torus (though it’s generally instructive and it is a prerequisite for computing their sufficiently general equivariant cohomology) but I have never seen it made explicit anywhere else. If anyone has a reference, please drop me a note.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a (sketchy) pointer to

      • Severin Bunk, Principal -Bundles and Smooth String Group Models, arXiv:2008.12263

      diff, v40, current

    • Eventually I’d like to connect quantum contextuality, contextuality in categorical logics, and the axiomatic approaches to QFT.

      v1, current

    • Changed the function field analogon of a prime number: from x in F_p to x in F_q. Please check that this is correct.

      Axel Boldt

      diff, v40, current

    • a stub entry — for the moment just to make the link work

      v1, current

    • This page just had a couple of references, so I’ve added the idea and more references.

      I came to this subject via Lurie’s MO question. Isn’t it a shame that such a highly regarded mathematician reaching out to the categorical logic community doesn’t receive an answer from them?

    • created some minimum at Cardy condition.

      Back then some kind soul provided these cobordism pictures at Frobenius algebra. Is that somebody still around and might easily provide also the picture for the Cardy condition?

    • Requested clarification in the currently false/confusing entry universal+differential+envelope (sorry I couldn't do more: this will need someone more qualified than me). -- Benoit Jubin

    • Start to a page for the PhysLean project. This relates to the pages on Lean, and projects like the Xena project. To develop it further, an inclusion of exmples of results formalized.

      The title appears to have a space in it, and I’m not sure how to deal with this. I can investigate.

      Joseph Tooby-Smith

      v1, current

    • Created my own page

      Umberto Tarantino

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • prompted by a question by email, I have expanded at homotopy pullback the section on Concrete constructions by listing and discussing the precise conditions under which ordinary pullbacks are homotopy pullbacks.

      Most of this information is scattered around elswehere on the nLab (such as at homotopy limit and right proper model category) and I had wrongly believed that it was already collected here. But it wasn’t.

    • added references to Lean

    • I tried to start an entry called Fermat theory. Unfortunately I screwed up and forgot to capitalized "Fermat". Maybe a lab elf can clean up my mess?

      There are also lots of other obvious ways this page could be improved...
    • brief category:people-entry for hyperlinking references

      v1, current

    • I wrote something at meaning explanation, but I didn’t add any links to it yet because I’m hoping to get some feedback from type theorists as to its correctness (or lack thereof).

    • Decidable language =/= decidable type checking.

      Arvid Marx

      diff, v23, current

    • (…)

    • Jotted down some things. Leibniz should feature but perhaps another day.

      diff, v6, current

    • Added a reference to

      • John W. Gray, Coherence for the Tensor Product of 2-Categories, and Braid Groups , pp.62-76 in Heller, Tierney (eds.), Algebra, Topology, and Category Theory , Academic Press New York 1976.

      diff, v19, current

    • started bracket type, just for completeness, but don’t really have time for it

    • 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.