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nLab > Latest Changes: bounded geometric morphism

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2010

    started stub for bounded geometric morphism

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 9th 2016

    I corrected the characterisation of boundedness.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 9th 2016

    Why don’t you just say quotient of a subobject of …, instead of subquotient of a subobject of …?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 9th 2016
    • (edited Jan 9th 2016)

    Oh I see. It was fine as it was. I’ll roll back, but fix a typo.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 10th 2016
    • (edited Jun 10th 2016)

    Jonas Frey has kindly added some material to the Properties-section at bounded geometric morphism. I have touched the formatting a little and added some more cross-links with the entry internal sheaf.

    Notice that the entry is still waiting for somebody to complete two items in its Definition section!

    • CommentRowNumber6.
    • CommentAuthorJonasFrey
    • CommentTimeJun 13th 2016

    I filled in the holes in the definition by copying the missing parts from the elephant, and rephrasing a bit.

    The equivalent reformulations use terminology that needs to be defined, therefore I amended separating family, adding the definition of separating family in a fibration.

    The concept of gluing fibration still needs to be defined – probably by remarking on the page on Artin gluing that the appropriate projection is a fibration. I’ll come back to that maybe tomorrow.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 13th 2016

    Thanks!

    • CommentRowNumber8.
    • CommentAuthorjonsterling
    • CommentTimeNov 17th 2021

    I think that the statement about the gluing fibration should be ∂1 not ∂0 right? We are restricting the codomain fibration along the inverse image of the geometric morphism, not the domain functor. Right?

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2021
    • (edited Nov 17th 2021)

    We are talking about this line, supposedly).

    But ∂0 is the codomain, in usual simplicial conventions (remove the 0-vertex!)

    In any case, for the moment I have removed the symbol “∂0” (it’s not too illuminating and never appears again, anyway). Somebody should indicate the actual definition of that morphism!

    diff, v12, current

1 to 9 of 9

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