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

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

• a minimum, for the moment just so as to record some references on $Pin(2)$-equivariant homotopy theory (as kindly pointed out by David Roberts)

• I have spent some minutes starting to put some actual expository content into the Idea-section on higher gauge theory. Needs to be much expanded, still, but that’s it for the moment.

• Added (not very elegantly) the relation to Meyer-Vietoris sequence at Dold-Thom theorem.

• Somebody named Adam left a comment box a while ago at premonoidal category saying that naturality of the associator requires three naturality squares. I believe that this is true when phrased explicitly in terms of one-variable functors, but the slick approach using the “funny tensor product” allows us to rephrase it as a single natural transformation between functors $C\otimes C\otimes C\to C$. I’ve edited the page accordingly. I also added the motivating example (the Kleisli category of a strong monad) and a link to sesquicategory.

There is a comment on the page that “It may be possible to weaken the above make $(Cat,\otimes)$ a symmetric monoidal 2-category, in which a monoid object is precisely a premonoidal category”. However, the Power-Robinson paper says that “We remark that $(C \otimes -) : Cat \to Cat$ is not a 2-functor,” which seems to throw some cold water on the obvious approach to that idea. Was the thought to define a different 2-categorical structure on $Cat$ than the usual one, e.g. using unnatural transformations? It seems that at least one would still have to explicitly require centrality of the coherence isomorphisms.

• added some text and some references

• Robert Switzer, Algebraic Topology - Homotopy and Homology, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Vol. 212, Springer-Verlag, New York, N. Y., 1975 (doi:10.1007/978-3-642-61923-6)
• For now, a place to try putting some typing rules for proto CLF.

• added pointer to these two recent references, identifying further $L_\infty$-algebra structure in Feynman amplitudes/S-matrices of perturbative quantum field theory:

• Markus B. Fröb, Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories (arXiv:1803.10235)

• Alex Arvanitakis, The $L_\infty$-algebra of the S-matrix (arXiv:1903.05643)

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

• I have added to M5-brane a fairly detailed discussion of the issue with the fractional quadratic form on differential cohomology for the dual 7d-Chern-Simons theory action (from Witten (1996) with help of Hopkins-Singer (2005)).

In the new section Conformal blocks and 7d Chern-Simons dual.

• brief category:people-entry for hyperlinking references at gauged WZW model

• started gauged WZW model, but no content yet, am just recording some references…

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

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

• Tried to tidy up the entry a little.

• This page proposes a notion of split pushout (of epimorphisms) that is then an absolute pushout “for equational reasons.”

• I noticed that we had no entry density, so I very briefly created one. While cross-linking it, I noticed that at volume form there is related discussion re “pseudo-volume forms”. Maybe somebody here would enjoy to add a bit more glue? (I won’t at the moment.)

• Has anyone written down an analogue for $(\infty,1)$-toposes of the (hyperconnected, localic) factorization system for 1-toposes? In particular, is it known that $n$-localic $(\infty,1)$-toposes form a reflective subcategory of all $(\infty,1)$-toposes?

• some minimum