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nLab > Latest Changes: regular epimorphism

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 26th 2021

    added pointer to:

    diff, v38, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 26th 2021

    added pointer to:

    diff, v38, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2021

    made some edits and additions. But have to rush offline now. Will polish and announce properly tomorrow…

    diff, v39, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2021
    • (edited Nov 9th 2021)

    So, I have tried to clean up this entry by adding more numbered environments for the various definitions and statements and more cross-links between them.

    For the proposition that regular epis with kernel pairs are effective epis I have adjoined the reference to Taylor 1999 by one to Borceux 1994.

    Then I made explicit the resulting statement and proof (here) that in a regular category effective epis are preserved by pullback.

    (Should copy much of this over to effective epimorphism, too.)

    diff, v40, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2021

    So, I have tried to clean up this entry by adding more numbered environments for the various definitions and statements and more cross-links between them.

    For the proposition that regular epis with kernel pairs are effective epis I have adjoined the reference to Taylor 1999 by one to Borceux 1994.

    Then I made explicit the resulting statement and proof (here) that in a regular category effective epis are preserved by pullback.

    (Should copy much of this over to effective epimorphism, too.)

    diff, v40, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2022

    added pointer to

    for the claim that every epimorphism in a topos is regular

    diff, v42, current

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 31st 2024

    the usual procedure is to consider the smallest class of arrows inside regular epis of which all pullbacks exist, namely the surjective submersions.

    This seems like a silly mistake: the smallest such class of arrows is the class of isomorphisms, or probably even the class of identity morphisms, if we don’t require isomorphism invariance.

    I have changed this to “largest class of arrows”

    diff, v45, current

1 to 7 of 7

  1.