Add “coterminator” to list of possible names.

]]>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?

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

]]>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 .

]]>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…

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

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

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