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    • seeing Eric create diffeology I became annoyed by the poor state that the entry diffeological space was in. So I spent some minutes expanding and editing it. Still far from perfect, but a step in the right direction, I think.

      (One day I should add details on how the various sites in use are equivalent to using CartSp)

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

      v1, current

    • Moving discussion here and summarizing content in the text

      +– {: .query} Mike: Why only rings without units (that is, rngs)? Intuitively, what important properties do the above listed examples share that are not shared by rings with units?

      Zoran Skoda: I want to know the answer as well. It might be something in the self-dual axioms. For unital rings artinian implies noetherian but not other way around; though the definitions of the two notions are dual.

      Toby: The category of unital rings and unitary ring homomorphisms has no zero object.

      Mike: Ah, right. Is it protomodular? I think I will understand this definition better from some non-examples that violate each clause individually.

      walt: It is protomodular. This follows from the main theorem of Characterization of Protomodular Varieties of Universal Algebra by Bourn and Janelidze. By that theorem any variety that contains a group will be protomodular. Unital rings only fail to be semiabelian for the trivial reason that ideals aren’t subrings.


      Maybe the result on protomodularity (with citation) mentioned by walt citing Bourn and Janelidze should be moved to CRing (and also Ring, if it holds for non-commutative rings).

      diff, v34, current

    • Added link to Bourn’s most helpful 2017 textbook From Groups to Categorial Algebra : Introduction to Protomodular and Mal’tsev Categories. Revised reference to the Borceux-Bourn 2004 monograph.

      diff, v8, current

    • a brief stub, to make links work

      v1, current

    • a bare list of references, to be !include-ed into the References-list of relevant entries

      v1, current

    • Modulo the definition, I’ve created Picard scheme. One thing I couldn’t tell, is there a standard term in nlab for the “fiber category” of a stack? I mean if F:CDF:C\to D fibers CC over DD then if you pick some object XX from DD the category C XC_X consisting of objects that go to XX and morphisms that go to id Xid_X.

    • I added some material to Mal’cev variety, namely proofs showing the various characterizations are equivalent, and a brief Examples section.

    • Added a PDF link for the original article by Malcev.

      diff, v3, current

    • I changed back the name of the page to coherent state. Though it is usually considered in quantum mechanics, and the name is still correct, as a specialist in the area of coherent states, I have almost never seen the phrase “coherent quantum state” written out in mathematical physics, so I would prefer to have this long unusual name as a redirect only. Of course, we often talk about the coherence of quantum states. But this is about a general feature of coherence, like in optics. The specific states in mathematical physics which, among other features, have such coherence properties are usually called squeezed coherent states, and the coherent states of these entry are even more specific than those. I am about to add a couple of new references, so I came across the page again.

      diff, v15, current

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


      v1, current

    • started a Properties-section at Lawvere theory with some basic propositions.

      Would be thankful if some experts looked over this.

      Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

    • At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group π 2(X,A)\pi_2(X,A) together with the bundary map δ:π 2(X,A)π 1(A)\delta:\pi_2(X,A)\to \pi_1(A) and the π 1(A)\pi_1(A)-action on π 2(X,A)\pi_2(X,A). As someone confirms this example is correct I’ll add it to crossed module.

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

      v1, 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.

    • I added to field a mention of some other constructive variants of the definition, with a couple more references.

    • This needs an entry of its own (currently hidden in a subsection of anomalous magnetic moment).

      Just starting something here, from my phone over coffee. More later.

      v1, current

    • this has been seen over 4σ4\sigma for a while now; time to record some references and to relate to flavour anomaly.

      Just starting here, from my phone over coffee. Nothing much to see here yet.

      v1, current

    • Stub. For the moment just for providing a place to record this reference:

      • Jean Thierry-Mieg, Connections between physics, mathematics and deep learning, Letters in High Energy Physics, vol 2 no 3 (2019) (doi:10.31526/lhep.3.2019.110)

      v1, current

    • splitting this off from Cohomotopy to make room for discussion of the Sullivan models from

      • Jesper Møller, Martin Raussen, Rational Homotopy of Spaces of Maps Into Spheres and Complex Projective Spaces, Transactions of the American Mathematical Society Vol. 292, No. 2 (Dec., 1985), pp. 721-732 (jstor:2000242)

      v1, current

    • As there had been a change to the entry for Ross Street I gave it a glance. Is there a reason that the second reference is to a paper without Ross as an author?I hesitate to delete it as there may be a hidden reason. (I have edited this discussion entry to remedy the point that Todd and Urs have made below. I also edited the title of this discussion!)

    • started adding something (the example of the Hopf fibration and some references).

      What’s a canonical reference on the Whitehead products corresponding to the Hopf fibrations? Like what is an original reference and what is a textbook account?

      diff, v11, current

    • a bare list of entries, for ease of cross-linking these in their lists of Related entries

      v1, current

    • starting some minimum on Hashimoto et al.’s D4-brane matrix model for baryons/nuclei in the WSS model for QCD

      v1, current

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

      v1, current

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

      v1, current