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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2015
    • CommentRowNumber2.
    • CommentAuthorNikolajK
    • CommentTimeDec 23rd 2015

    Makes me think of when is one thing equal to some other thing?.

    The formulation of the second law on the Wikipedia page is something I haven’t encountered, a¬aa\neq\neg a.

    Makes me wonder if a(a0)a\cong(a\to 0), e.g. in particular *(*0)*\cong(*\to 0), doesn’t make sense somewhere.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeDec 24th 2015
    • (edited Dec 25th 2015)

    In the setting of a category with zero object you have A(A0)A\simeq (A\to 0). I guess one should point to AT-category.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 25th 2015

    David, could you explain what you meant in your last comment? What is meant by A0A \to 0?

    A side remark is that any cartesian closed category with zero object 00 is trivial (i.e., equivalent to the terminal category). For any object AA we have A×00A \times 0 \cong 0 since 00 is initial and A×A \times - has a right adjoint; we also have A×0AA \times 0 \cong A since 00 is terminal. Thus A0A \cong 0 for every AA.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeDec 25th 2015
    • (edited Dec 25th 2015)

    Sorry, I was using Nikolaj’s notation (at least as I guessed what it meant): A0A \to 0 is the function type, ie Hom(A,0)Hom(A,0)…… ./… ….



    Blerg, obviously wrong. Never mind, it was just some random emission… :-/ (Edit: Was travelling last night on the train at the end of a long day of travelling, and didn’t think before I posted)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2022
    • (edited Sep 23rd 2022)

    added the following to the list of references:

    In Gottfried Leibniz’s unpublished but famous manuscript on logic (from some time in 1683-1716), reproduced In English translation in

    • Clarence I. Lewis, Appendix (p. 373) of: A Survey of Symbolic Logic, University of California (1918) [pdf]

    it says, after statement of the identity of indiscernibles and then the indiscernibility of identicals, that

    AA and AA are, of course, said to be the same

    diff, v3, current