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    • definition of affine monad from Jacobs

      v1, current

    • copied from HoTT wiki

      Anonymous

      v1, current

    • category: people page for references

      Anonymouse

      v1, current

    • category: people page for references

      Anonymouse

      v1, current

    • Balancing doesn’t mention duals anywhere, and makes sense even without duals. I removed an incorrect statement and replaced it with the correct one. Not sure if it needs a reference, but the correct result appears as Lemma 4.20 in https://arxiv.org/pdf/0908.3347.pdf (where it’s attributed to Deligne, but the citation is to Yetter).

      diff, v7, current

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

      v1, current

    • copied from the HoTT wiki

      Anonymous

      v1, current

    • Link to Wikipedia was dead. Maybe the page was moved to replace a short “-” in the title by a longer “–”?

      diff, v2, current

    • Creating page, adding content soon (in parallel with other pages).

      v1, current

    • Hello ncatlab.org,

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      Tamika Bolivar

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Created page, mainly to record/redirect the alternate name “elementary existential doctrine” and some references.

      v1, current

    • added at TC some references on computing THH for cases like koko and tmftmf, here

    • brief category:people-entry for hyperlinking references

      v1, current

    • 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.

    • added under “Selected writings” the articles cited elsewhere on the nLab

      diff, v2, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Some ×\times were written as xx, so fixed. There were sign changes going on that I didn’t understand, p 2(12p 2) 2p_2 - (\frac{1}{2}p_2)^2 and p 2+(12p 1) 2p_2 + (\frac{1}{2}p_1)^2.

      diff, v45, current

    • [deleted]

    • I fixed a link to a pdf file that was giving a general page, and not the file!

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

      Anonymous

      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.

    • Mention the Yoneda embedding/free cocompletion which was somehow not referenced before.

      diff, v13, current

    • In the definition, the article states "every object in C is a small object (which follows from 2 and 3)". The bracketed remark doesn't seem quite right to me, since neither 2 nor 3 talk about smallness of objects. Presumably this should better be phrased as in A.1.1 of HTT, "assuming 3, this is equivalent to the assertion that every object in S is small".

      Am I right? I don't (yet) feel confident enough with my category theory to change this single-handedly.
    • I added a little bit of material to ordered field, namely that a field is orderable iff it is a real field (i.e., 1-1 is not a sum of squares). More importantly, at real closed field, I have addressed an old query of Colin Tan:

      Colin: Is it true that real closure is an adjoint construction to the forgetful functor from real closed fields to orderable fields?

      by writing out a proof (under Properties) that indeed the forgetful functor from category of real closed fields and field homomorphisms to the category of real fields and field homomorphisms has a left adjoint (the real closure). Therefore I am removing this query from that page over to here.

    • Added material on diagonal maps and the product functor, mentioning for instance the fact that the product functor is right adjoint to a diagonal functor.

      diff, v22, current

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

    • concerning the discussion here: notice that an entry rig category had once been created, already.

    • Added a lemma about fully faithful functors.

      Sorry for the mess, there does not seem to be a way to preview edits.

      diff, v3, current