Oh now I see, sorry for being slow, thanks for insisting.

I have fixed that typo now

(that sentence is just narrating the little diagram that follows, here)

]]>I completely agree that $L,R$ are not the same between the sections on pairs and triples.

I am strictly not understanding the triples section:

]]>$L \;\dashv\; C \;\dashv\; R \,\quad\quad(12)$

…

Notice that in the case of an adjoint triple (12), the adjunction unit of $C\;\dashv\;R$ and the adjunction counit of $L\;\dashv\;R$ …

No, that’s what I tried to clarify (but clearly I failed):

The “$L$” and “$R$” in the sentence on adjoint triples are not the same “$L$” and “$R$” as in the previous sentence on adjoint pairs.

Let me try to reword further…

]]>The new wording is much better; unfortunately I still don’t quite follow the notation used in the paragraph following your revision.

As I understand it (in layman’s terms) adjoint functors $F\;\dashv\; G$ are a pair of functors between categories **with $G$ mapping in the opposite direction as $F$**, such that $F$ and $G$ have some special properties. As the page on adjoint triples shows, in a triple, the first and last functors map between the same categories. In our case we have that $L\;\dashv\; C\; \dashv \; R$, hence this would mean that $L, R: \mathcal{C}_1 \rightarrow \mathcal{C}_2$. Therefore does it make sense to talk about the adjunction “$L\;\dashv\; R$”? If so then the content might not be reflecting this to an unfamiliar audience.

I have edited Remark 1.34 now (here), thanks for pointing this out.

I did mean to use the symbols as I did (so that “$L$” is always the Leftmost, “$R$” the Rightmost), but I can see how it may be confusing. So I have now adjusted the wording around it.

]]>Thanks for fixing typos etc.! I appreciate it.

As for accumulated or smaller revisions: I may find smaller revisions easier to follow and to react to, but whatever works for you.

]]>There was also one more correction, but as I wasn’t certain and hence decided against making it:

[v47] In Remark 1.34, between (12) and (13): I think $L\;\dashv\;R$ should read $L\;\dashv\; C$.

I am generally inexperienced with the content in the site (I come from a background in physics but left academia after my masters). I am using the Geometry of Physics series as my main source towards learning mathematical physics in my spare time. Therefore, will likely find more typos and mistakes along the way. I still don’t fully understand adjoints, hence my hesitation to make this particular change.

As a general rule would it be better for me to comment on the forums on what I think is wrong and let more experienced members change it? I originally thought my diff would be manually verified as I “hadn’t been vetted”, and am now generally afraid to make an incorrect correction in the future that just gets pushed globally. If I am still “encouraged” to make the changes myself, is there any preference towards accumulating errors over a larger period of time and making a single revision, or are more frequent smaller revisions ok?

]]>Just made my first batch of edits on the site!

I thought the edits were more or less trivial so I didn’t make comments then, but seeing the discussion I have annotated them below to match the previous records:

- fixed the diagram in remark 1.28 where the labelling for the rightmost morphism was incorrect.
- fixed the first diagram of definition 1.33, where the categories had been incorrectly labelled given the morphisms used later on.
- fixed some misc typos and corrected weird wording

Thanks for chasing typos! I appreciate it.

]]>- fixed lemma 1.68 and proposition 1.69 where the induced adjoint modality is in the wrong order
- fixed the last diagram in the proof of proposition 1.77 where the leftmost functor is incorrectly labelled id instead of L
- fixed the first diagram in the proof of lemma 1.68 where the morphism LCRCLX -> RCLX should be \epsilon^\bigcirc, instead of \eta^\bigcirc

CanaanZhou

]]>Yes, thanks for catching this! Fixed now (here).

]]>Another thing. Definition 1.41 contains the diagram

$f \;=\; \eta_c \circ R(\widetilde f) \phantom{AAAA} \array{ && c \\ & {}^{\mathllap{\eta_c}}\swarrow && \searrow^{\mathrlap{f}} \\ R(L(c)) &&\underset{R (\widetilde f)}{\longrightarrow}&& R(d) \\ \\ L(c) &&\underset{ \widetilde f}{\longrightarrow}&& d }$

but clearly the equation on the left doesn’t match the diagram on the right; I think that the order of composition should be reversed.

]]>Yes, thanks for catching this! Fixed now (here).

]]>Hello,

This page says, in example 1.36

These hence form an adjoint triple

$Disc \;\dashv\; U \;\dashv\; coDisc \,.$Hence the adjunction unit of $Disc \dashv U$ and the adjunction counit of $U \dashv coDisc$ exhibit every topology on a given set as “in between the opposite extremes” of the discrete and the co-discrete

$Disc(U(X)) \overset{\epsilon}{\longrightarrow} X \overset{\eta}{\longrightarrow} coDisc(U(X)) \,.$

But this seems to be backwards? I think it should instead say

Hence the adjunction counit of $Disc \dashv U$ and the adjunction unit of $U \dashv coDisc$ exhibit every topology on a given set as “in between the opposite extremes” of the discrete and the co-discrete

I find the concept of adjunctions confusing so I am not sure.

Adrian

]]>There was still a left/right mixup in statement/proof of this Prop.. Hope to have fixed it now.

]]>Thanks for catching this! Yes, the order if $i^\ast$ and $r^\ast$ in equation (6) was wrong. Should be fixed now.

]]>Not sure which page this on after the split, but something needs fixing in Example 1.24. Is it just equation (6)?

]]>Since the page *geometry of physics – categories and toposes* did not save anymore, due to rendering timeouts caused by its size, I have to decompose it, hereby, into sub-pages that are saved and then re-!included separately.

With our new announcement system this means, for better or worse, that I will now have to “announce” these subsections separately. Please bear with me.

]]>