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nLab > Latest Changes: fixed point of an adjunction

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2015
    • (edited Sep 3rd 2015)

    created fixed point of an adjunction, just minimally so that it is possible to link to it.

    It seems strange that we wouldn’t have already an nLab entry on this, but after checking it seems to me that we didn’t.(?)

    Needs to be expanded…

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 3rd 2015

    At nucleus of a profunctor we have

    The nucleus of F is the center of this adjunction.

    Presumably that ’center’ is the fixed point.

    Don’t people really talk of the fixed subcategories of the adjunction?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2015

    A quick poll today among an unrepresentive number of people who should know favored “fixed point”. But I am happy with any way to call this. Who says “center”?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 3rd 2015

    Simon Willerton apparently

    What we will actually be interested in the nucleus, which is the centre, or invariant part, of this adjunction.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeDec 19th 2017
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2018
    • (edited Jul 22nd 2018)

    added mentioning of Gelfand duality as an example (here)

    diff, v6, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 23rd 2018

    made the definition a more detailed proposition (now here)

    diff, v7, current

    • CommentRowNumber8.
    • CommentAuthormattecapu
    • CommentTimeMar 28th 2023

    Added remark about validity of the theorem/proof in general 2-categories

    diff, v11, current

    • CommentRowNumber9.
    • CommentAuthormaxsnew
    • CommentTimeMar 28th 2023

    Explain that there might be no fixed points of an adjunction.

    diff, v12, current

1 to 9 of 9

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