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    • Wrote a section on the associated monad at operad, in terms of the framework introduced under the section titled Preparation.

    • I am splitting off Zariski topology from Zariski site, in order to have a page for just the concept in topological spaces.

      So far I have spelled out the details of the old definition of the Zariski topology on 𝔸 k n\mathbb{A}^n_k (here).

    • starting page on endomorphism monoid objects, to generalize endomorphism monoids and endomorphism rings

      Anonymous

      v1, current

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

      v1, current

    • Mentioned a characterisation of exponentiable multicategories.

      diff, v33, current

    • starting page on dependent type theory with type variables

      Anonymouse

      v1, current

    • tried to bring the entry orientation into a bit of shape

    • added this quote:

      Have no respect whatsoever for authority; forget who said it and instead look at what he starts with, where he ends up, and ask yourself, “Is it reasonable?”

      diff, v8, current

    • I expanded Maxwell’s equations by adding the integral form in SI system and then a shorter version of discussion from electromagnetism for the differential form of the equations, both in 3d and 4d formulations. Note also that Ampère’s law is about producing magnetic field from current; while it is Maxwell’s equation, or Ampère-Maxwell which adds the term with the change of electric field, the main discovery of Maxwell. Some people nowdays say generalized Ampère’s law what I wrote, but I am not happy about it as the general form does not generalize it in the straightforward manner, but adds new physics what needs a separate attribution.

    • I noticed only now that the entry bimodule is in bad shape and needs some attention. For the moment I have added here a mentioning of the 2-category of algebras, bimodules and intertwiners and a pointer to the Eilenberg-Watts theorem.

    • at additive functor there was a typo in the diagram that shows the preservation of biproducts. I have fixed it.

      Also formatted a bit more.

    • a stub, for the moment just so as to record pointer to Simpson 12 where “resolution of the paradox” is claimed to be achieved simply by passing from topological spaces to locales

      v1, current

    • a stub, for the moment just as to satisfy links

      v1, current

    • in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity

    • Added more material to Boolean algebra, particularly the principle of duality and the connection to Boolean rings, and a wee bit of material on Stone duality.

      Stone duality deserves greater expansion, bringing out the dualities via ambimorphic (ahem, schizophrenic) structures on the 2-element set, and mentioning the connection to Chu spaces. Another day, another dollar.

    • brief category:people-entry for hyperlinking references

      v1, current

    • I’ll be working a bit on supersymmetry.

      Zoran, you had once left two query boxes there with complaints. The second one is after this bit of the original entry (this will change any minute now)

      The theory of supergravity is, as a classical field theory, an action functional on functions on a supermanifold XX which is invariant under the super-diffeomorphism group of XX.

      where you say

      Zoran: action functional is on paths, even paths in infinitedimensional space, but not on point-functions.

      I think you got something mixed up here. If XX is spacetime, a field on XX is the “path” that you want to see. The statement as given is correct, but I’ll try to expand on it.

      The second complaint is after where the original entry said

      many models that suggest that the familiar symmetry of various action functionals should be enhanced to a supersymmetry in order to more properly describe fundamental physics.

      You wrote:

      This is doubtful and speculative. There are many models which have supersymmetry which is useful in their theoretical analysis, but the same models can be treated in formalisms not knowing about supersymmetry. Wheather the fundamental physics needs a model which has nontrivial supersymmetry is a speculative statement, and I disagree with equating theoretical physics with one direction in “fundamental physics”. I do not understand how can a model suggest supersymmetry; it is rather experimental evidence or problems with nonsupersymmetric models. Also one should distinguish the supersymmetry at the level of Lagrangean and the supersymmetry which holds only for each solution of the equation of motion.

      I’ll rephrase the original statement to something less optimistic, but i do think that supersymmetry is suggsted more by looking at the formal nature of models than by lookin at the nature of nature. If you have a gauge theory for some Lie algebra (gravity, Poincaré Lie algebra) and the super extension of the Lie algebra has an interesting classification theory (the super Poincar´ algebra) then it is more th formalist in us who tends to feel compelled to investigate this than the phenomenologist. Supersymmetry is studied so much because it looks compelling on paper. Not because we have compelling phenomenological evidence. On the contrary.

      So, if you don’t mind, I will remove both your query boxes and slightly polish the entry. Let’s have any further discussion here.

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting a category:reference-entry.

      Just a single item so far, but this entry should incrementally grow as more preprints appear (similar to what we have been doing at Handbook of Quantum Gravity and similar entries).

      I know that a soft deadline for submissions of at least one of the sections is this December, so I am guessing this is planned to appear in 2024.

      v1, current

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

      Anonymous

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • have added a minimum on the level decompositon of the first fundamental rep of E 11E_{11} here.

    • Added some references for surjections in homotopy type theory

      diff, v36, current

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

      Anonymous

      v1, current

    • There was a section about W-suspensions titled “Higher inductive types generated by graphs” in the article coequalizer type, so I moved the section into its own page at W-suspension.

      v1, current

    • Created this article on graph quotients using material split from W-suspension. The “W-suspensions in the first sense” in that article are actually called graph quotients in

      v1, current

    • This alone would not be an improvement over point particle versions of quantum gravity except that it is possible to define a perturbative expansion of string theory around a fixed, classical background space-time that is finite and anomaly free at 1-loop

    • starting something – just a bare minimum for the moment

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have added to continuum a paragraph titled In cohesive homotopy type theory.

      This is a simple observation and idea that I have been carrying around for a while. Several people are currently thinking about ways to axiomatize the reals in (homotopy) type theory.

      With cohesive homotopy type theory there is what looks like an interesting option for an approach different to the other ones: one can ask more generally about line objects 𝔸 1\mathbb{A}^1 that look like continua.

      One simple way to axiomatize this would be to say:

      1. 𝔸\mathbb{A} is a ring object;

      2. it is geometrically contractible, Π𝔸≃*\mathbf{\Pi} \mathbb{A} \simeq *.

      The last condition reflects the “continuumness”. For instance in the standard model Smooth∞Grpd for smooth homotopy cohesion, this distibuishes 𝔸=ℤ,ℚ\mathbb{A} = \mathbb{Z}, \mathbb{Q} from 𝔸=ℝ,ℂ\mathbb{A} = \mathbb{R}, \mathbb{C}.

      So while this axiomatization clearly captures one aspect of “continuum” very elegantly, I don’t know yet how far one can carry this in order to actually derive statements that one would want to make, say, about the real numbers.

    • added pointer to:

      • Albrecht Bertram, Stable Maps and Gromov-Witten Invariants, School and Conference on Intersection Theory and Moduli Trieste, 9-27 September 2002 (pdf)

      diff, v26, current

    • Added content, including the idea, GW/PT/GV correspondence and references. (The german Wikipedia article is now also available.)

      (I also plan to create an article for the Pandharipande-Thomas invariant in the future.)

      diff, v4, current

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

      Anonymous

      v1, current

    • felt like adding a handful of basic properties to epimorphism

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