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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• I have added the characterization of Quillen equivalences in the case that the right adjoint creates weak equivalences, here.

• I made the former entry "fibered category" instead a redirect to Grothendieck fibration. It didn't contain any addition information and was just mixing up links. I also made category fibered in groupoids redirect to Grothendieck fibration

I also edited the "Idea"-section at Grothendieck fibration slightly.

That big query box there ought to be eventually removed, and the important information established in the discussion filled into a proper subsection in its own right.

• I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?

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

• for completeness, I have copied over and dualized the definitions and some of the properties of generalized cohomology to the entry generalized homology.

• Changed “Kevin Costelli” to “Kevin Costello”.

Anonymous

• Martín Escardó and Paulo Oliva, Selection Functions, Bar Recursion, and Backward Induction, (pdf)
• The article wrote “locally ∞-presentable (∞,1)-category” when I’m sure $\kappa$-presentable was meant.

• added some basics to sequential spectrum: definition, $sSet^{\ast/}$-enrichment, statement of equivalence to $sSet^{\ast/}$-enriched functors on standard spheres and of Quillen equivalence to excisive $sSet^{\ast/}$-functors on $sSet^{\ast/}_{fin}$.

(This is a digest of more detailed discussion that I am typing into model structure for excisive functors.)

• To fix a grey link.

Anonymous

• starting something on unoriented cobordism with framed boundaries (using material adapted from MUFr). Not done yet, but need to save

• a bare table, to be !include-ed under “Related entries” in pertinent entries

Am trying to bring some order into the mess of entries of cobordism cohomology theories…

• I suppose with all the entries on Witten genus and related what was missing was an entry titled Dirac-Ramond operator. So I created one and filled in a bare minimum.

• 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 $X$ which is invariant under the super-diffeomorphism group of $X$.

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 $X$ is spacetime, a field on $X$ 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 a subsection “Properties – As algebraic K-theory over the field with one element” (here)