Re: Equality as an adjunction

[David Leduc <david.leduc6@googlemail.com>]

Do you mean that I am *all* wrong when I spell out the adjunction?

Anyway, I will definitely read Lawvere's papers on the topic and maybe
your thesis although I am a bit scared by this fibrational setting.

On Sat, Sep 4, 2010 at 3:09 PM, Robert Seely <rags@math.mcgill.ca> wrote:
> I *really* suggest you look at Lawvere's papers (and I also suggest
> you might find my elaboration of these ideas helpful).  What is going
> on here is essentially adjunctions (for sum and product, or
> equivalently existential and universal quantification) to
> substitution.  This sort of setup occurs in a fibrational setting, and
> the functors involved are between fibres;  the underlying common story
> is more compelling than just one example can suggest, I think.
>
>  - all the best, Robert
>
> On Sat, 4 Sep 2010, David Leduc wrote:
>
>> Sorry, I guess my mistake is that I've got the adjunction in the wrong
>> direction: it is a left Kan extension:
>>
>>  [CxC,2](Lan_Delta P, Q) =~ [C,2](P, Q o Delta)
>>
>> And equality is given by Lan_Delta T : CxC -> 2.
>> Does it always exist?
>>
>> And what was the right Kan extension in my previous mail when it exists?
>>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]