Add 1 as a notation for identity
Remove ─ as a notation for identity

As per Mike Shulman's request:

1 is good, if it doesn't cause conflicts.  "HomFunctor D ⟨ F^op ⟨ 1 ⟩ ,
1 ⟩ ≅ HomFunctor C ⟨ 1 , G ⟨ 1 ⟩ ⟩ looks fine to me.  It's actually
fairly common in category theory to write D(F,1) and C(1,G) for these
profunctors, as special cases of the general notion C(F,G) for two
functors F,G with the same codomain.

On Sun, Sep 15, 2013 at 11:26 AM, Jason Gross <jasongross9@gmail.com>
wrote:
> Ok.  I'll go use 1 instead, unless that's also bad.
>
> The reason I started using that was because I was trying to make
> notations like "Hom(F(─), ─)" work (and I did eventually get my
> notations working, so that I use "HomFunctor D ⟨ F^op ⟨ ─ ⟩ , ─ ⟩ ≅
> HomFunctor C ⟨ ─ , G ⟨ ─ ⟩ ⟩" as the type of hom-set adjunctions ---
> though, thinking back on it, I'm wondering about the op, and if things
> on the left should always be op'ed).  I tried using ( and ), but that
> interfered with ordered pairs, so I switched to ⟨ and ⟩.  The only way
> I could get it to work nicely was treating everything as functors; "G
> ⟨ ─ ⟩" is just G, and "F ⟨ G ⟨ ─ ⟩ ⟩" is "F ∘ G", so "F ⟨ foo ⟩" has
> to mean "F ∘ foo", and so the natural choice is to make "─" mean the
> identity functor.  This also works well with the choices needed for
> making commas work.  But I can switch to using 1 rather than ─ in most
> places.
>
> -Jason
>
>
> On Sunday, September 15, 2013, Michael Shulman wrote:
>>
>> Please don't use ─ for the identity functor.
>>
Get rid of some useless '∘ 1'