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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2011
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 7th 2011

    There’s no reason to restrict this definition to the cartesian case, is there? It seems to make sense for any closed (symmetric?) monoidal category — or maybe even any closed category.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2011
    • (edited Dec 7th 2011)

    Sure, but creating this entry was motivated from figuring out how precisely the term “strong” here is used in “classical” literature. Of course we can point that out in the entry and still generalize it.

    Also the variant [f !X,Y]f *[X,f *Y][f_! X, Y] \simeq f_* [X, f^* Y] deserves be called “strong adjunction”, it seems.

    I am agnostic about this. All I want eventually is to avoid that people interrupt my talks saying that I use “strong” in a bad way. :-)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeDec 8th 2011

    I’ve seen “strong” used in something like this way in the monoidal case as well. For instance we have strong functors and monads.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 8th 2011

    All I want eventually is to avoid that people interrupt my talks saying that I use “strong” in a bad way. :-)

    Yes, because there seems to be nothing categorists like more than a long, drawn-out terminological debate! Witness the discussion on the categories list on schizophrenic objects (again!).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2011

    I know what you mean. But I should mention that the person who wondered about my use of “strong” did so in a very sensible and helpful way. And I agree that my use of the word was not optimal, and that I need to think about changing something.

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeDec 8th 2011
    • (edited Dec 8th 2011)

    Luc Illusie said somewhere that when he would submit a manuscript to his advisor, certain guy with the name Alexander Grothendieck, that the manuscript was returned full of red marks, at all levels, from the factual corrections, improvements of the proof, additional requests to the linguistic, stylistic remarks and even orthography and commas…He enjoyed that, but the new list of red marks reappeared after a thorough revision. At the end he ignored repeating a process after 2nd iteration or so, wanting to finish a process.

    It is always enjoyable to get suggestions for improvements unless they are too stiff requests to substantially slow down (or even stop) the creation or publishing process. I had once a referee who rejected the paper with only a long list of stylistic corrections and no single content disagreement (well one, but in which the referee was trivially wrong, by the textbook fact). A problem with discussions in publishing process is that the editor or the referee can simply ignore you and just act by decision and power of the will; in the current way the things work, they are not obligated to listen for a scientific argument, plus they can (somewhat justified, but not always) hide behind the vague value statements like “important”, “difficult” and alike. With current publication pressure in which too many try to publish prematurely, the editors have just more reasons, not to attend the details and ignore even on the level of superficial negative feeling.

    • CommentRowNumber8.
    • CommentAuthormaxsnew
    • CommentTimeJan 19th 2024

    Am I correct that this is the same as an enriched adjunction where we view the CCC as self-enriched?