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nLab > Latest Changes: full and faithful functor

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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 5th 2017

    I have added to full and faithful functor the fact that they are closed under pushouts in Cat, with references (thanks to MO twice).

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeJun 1st 2020

    Added the characterization via pullbacks

    diff, v17, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 19th 2020

    Updated references and included links to published versions

    diff, v18, current

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeDec 8th 2022

    Add a counterexample showing that the existence of some isomorphism is not sufficient to imply full faithfulness.

    diff, v21, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 9th 2022

    gave that remark a Remark-environment (here)

    diff, v22, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 1st 2023
    • (edited Apr 1st 2023)

    I was about to polish-up the following reference items that were listed in the entry. But on second thought it is unclear why these references should be listed here at all. Probably they all mention fully faithful functors in some way. But it does not make sense to list here random articles mentioning this basic concept.

    Therefore I am removing the following items from the entry. If anyone knows that and why they should be listed after all, let’s add them back with a comment on what we mean the reader to find there regarding ff functors:

    diff, v24, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 31st 2023

    Remark that IL⊣RI L \dashv R implies L⊣IRL \dashv I R when II is fully faithful, and link to dominant functor.

    diff, v25, current

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 31st 2023

    Corrected IRI R to RIR I.

1 to 8 of 8

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