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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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…

• 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”

• 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.