Thanks for looking into this!

I have taken the liberty to

rename to “Lorentz Lie algebra” for definiteness (keeping “Lorentz algebra”) as a redirect, of course

replace the context menu “Differential geometry” with that for “Lie theory”

Okay?

]]>Typo (3 -> d-1)

Avi Levy

]]>Fleshing out idea section

Avi Levy

]]>Adding a related concepts section

Avi Levy

]]>I am creating this entry to resolve a dangling entry in the Lorentz group entry.

Avi Levy

]]>This definition reproduces the definition from Version 2 of https://arxiv.org/abs/0807.1704.

In Version 3, Baez and Hoffnung added the requirement that the site is subcanonical, and even mentioned this correction in the arXiv comment:

43 pages, version to be published; includes corrected definition of “concrete site”

Why is this requirement necessary? And if it is, we should probably add it to the article.

]]>Yes, I agree, we should definitely mention it somehow. I guess Mike was thinking about what should be the default meaning of the term ’walking equivalence’; let’s disuss that a little further down the road!

Back to #5: I agree that as I stated it the representing functor is not unique, but I think we should strengthen the hypotheses a little to make it unique, at least up-to-something. I’ll have a think myself about how to do this a little later if nobody else gets to it; but if anyone has a preference for how to state it, please just go ahead,

]]>Added Whitney’s original paper.

]]>Deleted a note about topic subdivision that is no longer relevant.

]]>Walking adjunction.

]]>The walking equivalence is definitely worth a mention, though, even if the ’correct’ notion is the walking *adjoint* equivalence. Even if to point out it only works in some cases. Also, there’s connection to the HoTT definition of equivalence, where the information is packaged differently (an a priori distinct left and a right quasi-inverse etc), or some of the Riehl–Verity ideas around coherent adjunctions.

I had included ’unique’ in my edit to isofibration yesterday too, removed now.

]]>Thanks for the corrections! Writing very fast, as I have to due to circumstances, apologies!

Yes, if we could wait until I’m finished with the stuff I plan to add to Lack fibration before changing things with regard to walking equivalence vs walking adjoint equivalence, that would be great.

]]>Thank you, no idea why I added unique there; writing on automatic without thinking! What I meant by the scare quotes was that one can make a definition as Lack did originally and maybe it makes sense for some things, so is not really ’wrong’ in an absolute sense; but I don’t mind removing them.

]]>I actually think that “the walking equivalence” should *be* an adjoint equivalence. I can’t think of any context in which one would want to use the walking non-adjoint equivalence. However, for the moment I refrained from making that change myself.

Corrected the definition – there is more than one arrow $0\to 1$ and $1\to 0$ (e.g. $i\circ i^{-1}\circ i$), and the definition as stated didn’t imply that $\iota_0$ and $\iota_1$ are isomorphisms. Also, the representing functor $F$ is not unique.

]]>The lifting against the free-standing equivalence is not unique. Also fixed a bit of the wording around the error: no need for scare quotes since it actually was an error, and as you said it didn’t change the definition of fibration but the definition of the free-standing equivalence.

]]>Thanks for chiming in! Absolutely! My recent edits are mainly building up to adding some material to the new page Lack fibration and some material on canonical model structures on higher categories; I think the walking adjoint equivalence will be needed for this.

]]>Oh, cool. Nice to see you on the editorial board, Nora!

]]>Just because I’m marking exams and can’t think about this right now: might it be worth doing the walking adjoint equivalence? It would presumably be a quotient of Adj, and there might be an interesting relationship between the walking equivalence and the walking adjoint equivalence, seeing at equivalences can (generally?) be upgraded to an adjoint equivalence (see Theorem 3.3 as numbered in the current version), at the cost of perhaps changing part of the data.

]]>I took the liberty of replacing “arrow” with *1-morphism*, *2-morphism*, and *n-morphism*, where appropriate.

Adding redirect for ’interval groupoid’, and adding remark that the walking isomorphism is the free groupoid on the walking arrow, which was previously at interval category.

]]>Removing the redirect for interval groupoid, which will now go walking isomorphism instead. Tweaked and made more concise the section ’Interval groupoid’ accordingly; I will move the (small amount of) removed material to walking isomorphism.

]]>Jesper Michael Møller almost always goes by his full name, and if shortened, the middle initial is included.

Also add a reference to the classification of p-compact groups for $p$-odd.

]]>