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nLab > Latest Changes: inverse semigroup

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 30th 2015
    • (edited Nov 30th 2015)

    Added a bunch of material to inverse semigroup under subsections of “Properties”.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeDec 2nd 2015

    Interesting. What are you up to ?

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 2nd 2015

    The edits were spurred by some side research, when I was looking into an MO question which was shut down by some of the usual gatekeepers there, and which wound up being the “Warning” subsection. I learned enough about the topic to make some edits there, that’s all.

    However, it did reignite some possible interest in returning to my “cartologies” article on my personal web, which was left in limbo (like almost everything there, alas).

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeDec 2nd 2015

    Cartologies has been an interesting project!

    • CommentRowNumber5.
    • CommentAuthorJoshua Meyers
    • CommentTimeSep 1st 2019

    I just proved a “Cayley’s theorem” for inverse semigroups — that every inverse semigroup is isomorphic to a sub-semigroup of I(X) for some set X. Should I add this fact to the article? Should I also add a proof? I am new with contributing to the nLab so I don’t know how this works.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 1st 2019

    I say yes, to both things (and thanks). If anything else needs to be done, someone will come by.

    • CommentRowNumber7.
    • CommentAuthorJoshua Meyers
    • CommentTimeSep 1st 2019

    Adding a “Cayley’s theorem” for inverse semigroups to show that any inverse semigroup can be realized as a semigroup of partial bijections of a set. I’m not sure if this is the same as the Wagner-Preston theorem.

    diff, v19, current

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeSep 9th 2019
    • (edited Sep 9th 2019)

    Yes, it is called Wagner-Preston and not Cayley in this generalized setting, cf. https://en.wikipedia.org/wiki/Wagner-Preston_Theorem.

    • CommentRowNumber9.
    • CommentAuthorJoshua Meyers
    • CommentTimeDec 29th 2021

    Added reference to Wagner-Preston theorem

    diff, v24, current

  10. Fixed typo

    Anonymous

    diff, v25, current

    • CommentRowNumber11.
    • CommentAuthorTim_Porter
    • CommentTimeApr 3rd 2023

    Added redirect for ordered groupoid(s).

    diff, v27, current

1 to 11 of 11

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