Categories with specified pullbacks

Categories with specified pullbacks

[David Roberts]

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,

David

-- 
David Roberts
http://ncatlab.org/nlab/show/David+Roberts


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Re: Categories with specified pullbacks

[David Roberts]

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,
>


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