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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 1st 2017

    I added to initial object the theorem characterizing initial objects in terms of cones over the identity functor.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 1st 2017

    I drew the obvious corollary, that an object is initial iff it is the limit of the identity functor.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2018
    • (edited Jun 22nd 2018)

    I have cross-linked the discussion of initial objects as limits over identity functor here with the discussion at adjoint functor where this is put to use: there.

    Also, I added pointers to MacLane, lest any reader gets the impression that this weren’t in the literature…

    diff, v23, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2018

    By the way, if I were to decide, I would replace the writeup of the proof “initial object is limit over identity functor” in the entry by what is now in Sandbox 1528 .

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJun 23rd 2018

    Add a bit more explanation to “initial = limit of identity functor”

    diff, v24, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJun 23rd 2018

    The existing proof was admittedly a bit telegraphic in places; I added a bit more explanation that certain triangles commute by the cone condition. But in general I like the more concise version. However, the longer version could be on a breakout subpage?

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeJan 8th 2019

    Add “coterminator” to list of possible names.

    diff, v28, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2021

    added pointer to:

    diff, v31, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2021

    Prodded by a comment here I have clarified the wording (here) regarding strict initial objects.

    While I was at it I have added a bunch of Definition/Remark environments and re-arranged somewhat, for more systematics.

    The remaining examples of strict initial objects I have moved to strict initial object.

    diff, v34, current