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nLab > Latest Changes: well-pointed topos

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2010

    Added an "Examples"-section to well-pointed topos and to Boolean topos mentioning Set and models for ETCS.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2010

    started a section well-pointed (oo,1)-topos as parts of the blog discussion here

    In the course of that I added to the plain definition the statement that the global section functor is faithful

    • CommentRowNumber3.
    • CommentAuthorNikolajK
    • CommentTimeSep 12th 2020

    The pretopos section ends in a sentence I don’t know how to interpret:

    But of course it applies whenever one is studying a pretopos.

    Does this really mean topos here at the end? If not, what is “it”?

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 12th 2020

    I think the “it” means this bit:

    we have to strengthen the condition that 1 is a generator to the condition that 1 is a strong generator,

    And I think the “whenever” means that it’s not just in thinking about a predicative category of sets, but an arbitrary pretopos.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 12th 2020

    Clarified last paragraph of the section “In a pretopos”

    diff, v25, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeMar 4th 2021

    Fixed the last equivalent version of well-pointedness, and added a proof that 1 is also a strong generator.

    diff, v28, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeMar 4th 2021

    Added a proof that in classical logic, well-pointedness is equivalent to the conjunction nondegenerate + Boolean + two-valued + split supports. This seems to be hard to find in the literature.

    diff, v28, current

    • CommentRowNumber8.
    • CommentAuthorKeith Harbaugh
    • CommentTimeMar 5th 2021

    Added section “References”, at this time containing only some references to Mac Lane and Moerdijk’s SGL. Also added some remarks.

    diff, v29, current

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeMar 5th 2021

    Added citations for the recently added theorem, thanks to an anonymous contributor by email.

    diff, v33, current

  10. added a separate definition of well-pointedness in terms of the axiom schemata of bounded separation (in addition to the terminal object being a strong generator), as defined in

    Anonymous

    diff, v41, current

  11. added example of a coherent category satisfying the axiom of finiteness

    Anonymous

    diff, v44, current

1 to 11 of 11

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