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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