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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2010

    I edited subobject slightly and added the statement that in an accessible category CC every poset of subobjects is small.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010
    • (edited Dec 29th 2010)

    The collection of subobjects (in the sense of equivalence classes) may be a proper class, even in abelian categories. One related entry is property sup. (edit: added this link into “related entries”; btw, I do not understand listing the entry itself there).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2010

    The collection of subobjects (in the sense of equivalence classes) may be a proper class, even in abelian categories.

    Let’s see, is this meant to be in contradiction to saying that in an accessible category it is a set?

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeDec 30th 2010

    This is (if you read carefuly) an introductory statement to property sup which is about further restriction to the chains of subobjects, still intuitively surprising. I think that accessible abelian categories do not need to satisfy the property sup. I do not know what happens with the chain conditions when we talk about chains in a proper class. Dividing into accessible and nonaccessible does not solve the problem of understanding the behaviour of bounds on chains.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2011

    at subobject I have started a new Properties-subsection Limits and colimits of subobjects with some basics on joins/pushouts and meets/fiber products etc.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2011

    … and now also with the full proofs.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 11th 2012

    added list of basic examples to subobject.

    • CommentRowNumber8.
    • CommentAuthorTobyBartels
    • CommentTimeSep 1st 2018
    • (edited Sep 1st 2018)

    I removed redirects for subtype and subalgebra (and their plurals), since neither string ‘typ’ nor ‘gebr’ appears anywhere on the page.

    diff, v36, current

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeSep 2nd 2018
    • (edited Sep 2nd 2018)

    Actually, that edit didn't take. I keep getting Cloudfare HTTP errors. Interestingly, the last attempt did manage to break the redirects, even though it didn't save the new page source.