Re: Categories with specified pullbacks

[David Roberts <droberts.65537@gmail.com>]

Dear Peter,

Would you (or others on the list) happen to have an electronic copy of
"On canonizing category theory or on functorializing model theory"? A
document such as this (even cited in the Elephant!) should be more
widely available, I think. Even if subsumed by Categories, Allegories
it is of historical interest.

Thanks,

David

On 4 September 2017 at 19:41, Peter Freyd <pjf@seas.upenn.edu> wrote:
>
>
> Best thoughts,
>     Peter
>
>
> Begin forwarded message:
>
> From: Peter Freyd <pjf@upenn.edu>
> Date: September 3, 2017 at 11:59:26 AM EDT
> To: categories
> Subject: Re:  Categories with specified pullbacks
>
> In my book with Andre Scedrov, "Categories, Allegories," is a
> small-print diversion about "tau-categories," pages 54--67. (The
> material dates to the mid-70s.)
>
> Yes, it does provide choice-free constructions for several
> representation theorems, indeed, it provides choice-free
> constructions for (previously unknown) natural transformations
> between those representations.
>
> (While on the subject, take a look at "New entry [1.536]" on page 3 of
>
>   http://www.math.upenn.edu/~pjf/amplifications.pdf
>
> for quite another use, this one using a lot of "strictness.")
>
>  Best thoughts,
>    Peter
>
>
> ----- Original Message -----
> From: "David Roberts" <droberts.65537@gmail.com>
> To: "categories@mta.ca list" <categories@mta.ca>
> Sent: Wednesday, August 30, 2017 10:57:36 PM
> Subject: categories: Categories with specified pullbacks
>
> Dear all,
>
> I'm trying to track down a paper I once saw that I recall constructed,
> from a category with pullbacks, an equivalent category with
> *specified* pullbacks. I don't believe there was any strictness, in
> the sense that pulling back along fg was the same as the result of
> pulling back along one then the other. The feature I'm interested in
> is that I think that this construction required no global choice,
> except for one direction of the equivalence, which for me is no big
> deal. I may have misremembered this last bit, so I need to check the
> paper.
>
> Thanks,
>


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