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.

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