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nLab > Latest Changes: small presheaf

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 13th 2020
    • (edited May 13th 2020)

    Added a reference.

    Can we say exactly what kind of pretopos the category of small presheaves on a category C is?

    Is it a ΠW-pretopos, provided that PC is complete?

    diff, v9, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 13th 2020

    What is PC?

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 14th 2020

    PC is the notation used in the article for the category of small presheaves.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 14th 2020

    ok, thanks. I think the Π\Pi part is difficult. The WW part is easier. I don’t know offhand what PCPC being complete gets you.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeMay 20th 2020

    Yeah, I’d be doubtful that you can get lccc. Usually that sort of thing requires an adjoint functor theorem with small-generation hypotheses.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 30th 2023

    Updated the reference

    • Jiří Rosický Accessible categories and homotopy theory, lecture notes for the Summer School on Contemporary Categorical Methods in Algebra and Topology (2007) pdf

    as the pdf link was broken, and it only had title and author in a paragraph.

    diff, v11, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeApr 20th 2023

    Add a reference to “How large are left exact functors?”.

    diff, v13, current

1 to 7 of 7

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