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    • CommentRowNumber1.
    • CommentAuthorAlec Rhea
    • CommentTimeJan 31st 2019

    The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.

    diff, v19, current

    • CommentRowNumber2.
    • CommentAuthorAlec Rhea
    • CommentTimeJan 31st 2019

    I also added a few words in the definition section that seemed to be missing, apologies for the double post.

  1. No problem, I have tidied up the postings :-).

    • CommentRowNumber4.
    • CommentAuthorAlec Rhea
    • CommentTimeJan 31st 2019

    Much appreciated!

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeJul 11th 2021

    Mention terminology functor of effective descent type.

    diff, v23, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 12th 2022

    added some references:

    diff, v25, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 12th 2022
    • (edited Aug 12th 2022)

    have touched the formatting of this entry, in the hope of improving readability

    diff, v25, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 6th 2022

    I have hyperlinked all occurrences of “comparison functor” on this page, and am giving this is own page now.

    diff, v29, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023
    • (edited Apr 16th 2023)

    added the proposition (here) that monadic functors create limits

    (copied over from the created limit)

    diff, v30, current

    • CommentRowNumber10.
    • CommentAuthorvarkor
    • CommentTimeApr 30th 2023

    Add a cancellation result for monadic functors.

    diff, v31, current

    • CommentRowNumber11.
    • CommentAuthorJohn Baez
    • CommentTimeMay 4th 2023

    Added two properties of monadic functors: faithfulness and conservativity.

    diff, v32, current

    • CommentRowNumber12.
    • CommentAuthorJohn Baez
    • CommentTimeMay 5th 2023

    Added properties of monadic functors to Set.

    diff, v35, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2023
    • (edited Sep 2nd 2023)

    added (here) explicit mentioning of the example of reflective subcategory inclusions

    (also made some cosmetic edits to the corresponding proposition here at reflective subcategory, such as cross-linking with where it is mentioned in the text there)

    diff, v41, current

    • CommentRowNumber14.
    • CommentAuthorncfavier
    • CommentTimeOct 8th 2023

    The link to 1lab here and at reflective subcategory is broken; I don’t know whether it was intended to link directly to the relevant page or to a reference at the bottom of the page.

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2023

    Thanks for the heads up. After a little inspection, I see that something strange has been happening:

    The reference which the seemingly broken link points to is certainly present in the source code: see the very bottom of ncatlab.org/nlab/source/reflective+subcategory.

    But with revision 111 by “Gnampfissimo” the whole last third of the entry (most of the Examples-section, and all of the References) is marked in the logs as deleted and indeed no longer shows in the rendered page.

    Nevertheless, the code for all the seemingly deleted material is still visible in the source.

    So what gives?

    Turns out that this revision 111 by “Gnampfissimo” also changed

      +-- {: .num_example }
      ###### Example
    
      A category of [[concrete presheaves]] inside a [[category of presheaves]] on a [[concrete site]] is a reflective subcategory.
    
      =--
    

    to

      +-- {: .num_example }
      ###### Example
    
      A category of [[concrete presheaves]] inside a [[category of presheaves]] on a [[concrete site]] is a reflective subcategory.
    
      =--apocalypticists
    

    and apparently this triggers a bug in the rendering software which causes all following code to be ignored.

    I am not fixing this right now. Will first bring this in situ to the attention of technical team.

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2023
    • (edited Oct 9th 2023)

    Have fixed now the entry reflective subcatgory, see the discussion there.