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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeSep 12th 2013
    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 12th 2013

    Thanks. To be linked to injective hull at some point.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeSep 13th 2013

    Already, injective hull links to essential embedding, which redirects to essential ideal, but the meaning is different (although I'm sure related).

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 13th 2013
    • (edited Sep 13th 2013)

    Well, the idea of that redirect was to connect it to “essential extension” which was defined in essential ideal. (In a parenthetical aside, “essential embedding” was given as a synonym.) Do you think that’s confusing?

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeSep 13th 2013

    I see the connection, vaguely, but there is no definition of ‘essential embedding’ at essential ideal, and seeing the redirect makes me think that the inclusion map of submodules is the referent of ‘essential embedding’. Yet, that is not the referent at injective hull, so yes, it is confusing.

    In particular, at injective hull, ‘essential embedding’ seems to be something with a meaning in a concrete category, while the concepts at essential ideal apply to abelian categories. Even in a concrete abelian category, I doubt that these agree.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 13th 2013

    Oh, jeez. Yes; sorry. I can fix this a little later (but feel free to fix yourself now if you’d like).

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeSep 14th 2013

    I don't actually know how to fix this, (unless the redirect from essential embedding to essential ideal is just wrong, in which case I can undo that).

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