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• Fixed pdf link to “Towards an understanding of Girard’s transcendental syntax”

ALH

• I have changed the title of this article, as well as references to the object within it. Use of the term “Hawaiian Earring” is objected to by Hawaiian mathematicians. Please see these two threads, one by native Hawaiian and math PhD Dr. Marissa Loving, and the other by an expert on the Hawaiian Earring, Dr. Jeremy Brazas.

I have retitled the article “Shrinking wedge of circles”, which is the name used for this space in Hatcher’s “Algebraic Topology”. I have a retained a note in the body of the article that the space is sometimes referred to as the “Hawaiian earring space”.

This small change in name helps to make mathematics a more inclusive and just field, especially in consideration of the historical marginalization and exclusion of indigenous mathematicians. By taking this action, the nLab site can help to spread a change in language more widely, including on other math reference sites.

I hope that this change is readily accepted and approved by the nLab community. Thank you!

Justin Lanier

• Done, but now there is some overlap.

• Reorganization and expansion to consider constructive variants.

• Added a diagram at commutative algebraic theory using the totally awesome SVG Editor.

it now does itex!

This was a ridiculously simple diagram to do.

• Valentine Bargman, Note on Wigner’s theorem on symmetry transformations, Journal of Mathematical Physics 5.7 (1964): 862-868 (doi:10.1063/1.1704188)
• In the article connection on a cubical set the definition of a connection uses two types of maps, denoted Γ^+_i and Γ^-_i. Roughly, the former corresponds to a map of cubes that takes the minimum of some coordinates, whereas the latter takes the maximum of some coordinates.

However, in the book by Brown-Higgins-Sivera in Definition 13.1.3, page 446, only the maps Γ^-_i are used. There they are denoted simply by Γ_i. The paper by Maltsiniotis about the strict test category of cubes with connection also uses the same definition.

Which definition is correct? What is the reference for nLab’s definition and why does it deviate from the definition of Brown-Higgins-Sivera?

• In the past we had some discussion here about why simplicial methods find so much more attention than cubical methods in higher category theory. The reply (as far as I am concerned at least) has been: because the homotopy theory = weak oo-groupoid theory happens to be well developed for simplicial sets and not so well developed for cubical sets. Historically this apparently goes back to the disappointment that the standard cubical geometric realization to Top does not behave as nicely as the one on simplicial sets does.

Still, it should be useful to have as much cubical homotopy theory around as possible. Many structures are more naturally cubical than simplicial.

So as soon as the Lab comes up again (we are working on it...) I want to create a page model structure on cubical sets and record for instance this reference here:

• Add $\#$-connected for general inequalities.

I was chatting with Robin Cockett yesterday at SYCO1. In a talk Robin claims to be after

The algebraic/categorical foundations for differential calculus and differential geometry.

It would be good to see how this approach compares with differential cohesive HoTT.

• re-did the typesetting of the adjoint triple with TikZ

• tried to improve the entry coproduct a little

• I have touched the formatting at direct sum and then expanded a little:

1. Added a paragraph to the Idea-section such that something familiar is mentioned right at the beginning;

2. Expanded on the example of direct sums in $Ab$ by drawing the cocone diagrams and explicitly mentioning the universal property.

3. Mentioned the relation to formal linear combinations.

4. Mentioned the examples of direct sums of modules.

• New.

• added below the very first definition at kernel a remark that spells out the universal property more explicitly. Also added mentioning of some basic examples.

• added the Hurewicz model structure as an example of 2-trivial model structure

Daniel Teixeira

• Eventually I’d like to connect quantum contextuality, contextuality in categorical logics, and the axiomatic approaches to QFT.

• Since it was mentioned by Urs on g+, I thought I’d start mysterious duality. Maybe not a great name when someone discovers how it works (as someone claims to have done here).

• Included the more general definition of Cartan subalgebra from Nathan Jacobson’s book.

• brief category:people-entry for hyperlinking references

• stub

• stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.

• Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their interrelatedness. I wasn’t sure what to name this page — or even whether it should be part of some other page — but I like having all these closely related structures described in the same place.

• Added the adjective grouplike to A_infty space as else I just get a monoid object instead of a group object.

Anonymous

• changed page name to singular

• Corrected the definition.

• made some minor cosmetic edits, such as replacing

  \bar W G


(which comes out with too short an overline) with

  \overline{W} G

• for completeness, I have added pointer to

for proof of the Hausdorff property of CW complexes

• Redirect: loop functor.

• 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.
• added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)

• Max New: at (129.10.9.38) has put a query on the generalized universal bundle entry. It says:

I don’t understand the above diagram, what is the point $* \to X$ in question? and how does this relate to the universal bundle? In particular, there is a sequence below that has a map from $\Omega_{pt} \to \mathbf{E}_{pt}$ but I don’t see how to construct that from the above.

So I think this is a typo, but I don’t know enough to correct it.

• Add Kanamori reference (from David Roberts's blog)

• Added description of the representing object of $I$-indexed camilies of equicontinuous functions into $U$, and proof that the limit-selection function for convergent nets is continuous with respect to this uniformity.

• I created separator, while having the nagging feeling that we already have this entry. Of course after creating it I remembered the page generator.

So we should merge the stuff. Might this be an occasion to merge away from generator? A set of “generating objects” also means other things than “separating objects” (notably colimit generation). So I’d be inclined to move all material to separator. That would also allow to drop the warning at the beginning of generator.

• am splitting this off from Lie algebra, for ease of cross-linking.