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    • CommentRowNumber1.
    • CommentAuthorJoshua Meyers
    • CommentTimeDec 29th 2021
    • (edited Dec 29th 2021)

    Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor

    Todo: add more proofs of this result.

    For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:

    An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out

    How can I fix this?

    v1, current

    • CommentRowNumber2.
    • CommentAuthorJoshua Meyers
    • CommentTimeDec 29th 2021

    Typo fixes

    v1, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2021

    For the xymatrix to display, they must not be enclosed by any other environment and the delimiters must be aligned to the far left.

    (I was going to fix it, but, since last night, all attempts to submit tikzcd or xymatrix to the nnLab time out.)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2021

    Now the xymatrix is rendering. Also made the author links come out and added publication data.

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeDec 29th 2021
    Thanks!
    • CommentRowNumber6.
    • CommentAuthorJoshua Meyers
    • CommentTimeDec 29th 2021
    I just tried to do some typo fixes, but xymatrix is timing out again. Any idea what's happening?
    • CommentRowNumber7.
    • CommentAuthorJoshua Meyers
    • CommentTimeDec 29th 2021
    Just tried tikzcd instead...it still timed out. I know that it is not just a typo because I copied one of the example tikzcds from https://ncatlab.org/nlab/show/HowTo and that made it time out. Any suggestions?
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2021
    • (edited Dec 29th 2021)

    According to Richard here, the server has apparently reached the point where it can’t handle the size of the nnLab anymore, and we need to wait for Richard to, thankfully, migrate us to a better server.

    • CommentRowNumber9.
    • CommentAuthorRichard Williamson
    • CommentTimeDec 29th 2021
    • (edited Dec 29th 2021)

    I think editing this page may be triggering the problems, as it is deeply nested in the rest of the nLab, so it may be best to hold off for a while.

  1. Tweak diagrams to be centred on the page.

    v3, current

    • CommentRowNumber11.
    • CommentAuthorRodMcGuire
    • CommentTimeApr 21st 2022

    where do the sources for the tikzcd diagrams on this page live?

    The page source only has stuff like

    <img src="/nlab/diagrams/show/20220421002920849955">

  2. Answered here :-).

    • CommentRowNumber13.
    • CommentAuthorTim_Porter
    • CommentTimeApr 21st 2022

    I corrected the title of the first referenced paper. Thanks RIchard for all the work.

    • CommentRowNumber14.
    • CommentAuthorRichard Williamson
    • CommentTimeApr 21st 2022
    • (edited Apr 21st 2022)

    Great! So far the edits seem to have gone through fine. There is no diff functionality yet, but if people wish to see what has changed they can of course do so locally, e.g.:

    curl https://ncatlab.org/nlab/history/source/comprehensive%20factorization%20system/5 > /tmp/revision_5
    curl https://ncatlab.org/nlab/history/source/comprehensive%20factorization%20system/6 > /tmp/revision_6
    vimdiff /tmp/revision_5 /tmp/revision_6
    

    Here, for those who are not familiar with it, curl is just a command-line way to fetch the content of a webpage (or execute other HTTP methods), one can equally well visit the page and download the content.

  3. linked domain to nLab article on domains

    testing comments

    v7, current

    • CommentRowNumber16.
    • CommentAuthorvarkor
    • CommentTimeNov 2nd 2022

    Added a reference to The comprehensive factorization and torsors.

    diff, v4, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeNov 2nd 2022

    I have added pointer to the actual article: tac:23-03

    diff, v5, current

    • CommentRowNumber18.
    • CommentAuthorvarkor
    • CommentTimeMar 16th 2023

    Add some redirects.

    diff, v6, current

    • CommentRowNumber19.
    • CommentAuthorBryceClarke
    • CommentTimeApr 18th 2023

    Added doi links for several references.

    diff, v7, current

    • CommentRowNumber20.
    • CommentAuthorvarkor
    • CommentTimeOct 27th 2023

    Mention the mistake in the proof of Street–Walters.

    diff, v8, current

    • CommentRowNumber21.
    • CommentAuthorvarkor
    • CommentTimeDec 29th 2023

    Mentioned the dual.

    diff, v9, current

    • CommentRowNumber22.
    • CommentAuthorncfavier
    • CommentTimeJan 10th 2024

    I think an object of EE should be an ordered pair (d,[α:dFc])(d,[\alpha:d\to Fc]), not the other way around (since final functors talk about the comma categories d/Fd/F). Could someone double-check?

    • CommentRowNumber23.
    • CommentAuthorncfavier
    • CommentTimeJan 10th 2024

    It’s also unclear why “It suffices to consider the case of a zig-zag of length one”: the argument works by induction if every morphism in the zig-zag is between objects of the form FxFx, but that need not be the case.

    • CommentRowNumber24.
    • CommentAuthorncfavier
    • CommentTimeJan 10th 2024

    I guess the idea is that you can modify a zig-zag GFcGxGyGFcGFc \leftrightarrow Gx \leftrightarrow Gy \leftrightarrow GFc' to GFcGFxGFyGFcGFc \leftrightarrow GFx' \leftrightarrow GFy' \leftrightarrow GFc' using that each x/Fx/F is inhabited, and then the argument applies to this modified zig-zag.