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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 23rd 2018

    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.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 23rd 2018

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

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 23rd 2018

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

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2021

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

    diff, v40, current

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeMar 3rd 2023


    This page says, in example 1.36

    These hence form an adjoint triple

    DiscUcoDisc. Disc \;\dashv\; U \;\dashv\; coDisc \,.

    Hence the adjunction unit of DiscUDisc \dashv U and the adjunction counit of UcoDiscU \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))εXηcoDisc(U(X)). 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 DiscUDisc \dashv U and the adjunction unit of UcoDiscU \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.


    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2023

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

    diff, v43, current

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeMar 3rd 2023

    Another thing. Definition 1.41 contains the diagram

    f=η cR(f˜)AAAA c η c f R(L(c)) R(f˜) R(d) L(c) f˜ d 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.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 4th 2023

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

    diff, v45, current

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


    diff, v46, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMar 30th 2023

    Thanks for chasing typos! I appreciate it.