Re: opposite category

[Vaughan Pratt <pratt@cs.stanford.edu>]

Well, one could look to the various power set functors for guidance there.

When you refer to the contravariant power set functor, it may be
contrary but it's reliably so and people know what you mean.

But "the" covariant power set functor??? What's that??? It's like Trump:
one day he's agreeing with the Elephants, the next with the Scientific
Consensus.

If there are more than two covariant power set functors maybe we'll see
yet another side of Trump, perhaps a side from another dimension.

Give me good old reliable contravariant.???? Mind the pence and the
pounding will take care of itself.

Oh but wait, there's profunctors,?? ??: A' x B --> V.???? Which way do /they
/go? The Elephant
<https://www.amazon.com/Sketches-Elephant-Theory-Compendium-Oxford/dp/019852496X/ref=sr_1_1?ie=UTF8&qid=1505521975&sr=8-1&keywords=sketches+of+an+elephant>
(kindle edition $4.99
<https://www.amazon.com/Draw-Animals-Step-Step-Elephants-ebook/dp/B007WKEMBE/ref=sr_1_4?ie=UTF8&qid=1505522093&sr=8-4>)
says they go from A to B.?? The Consensus, being a bunch of Deniers, says
("bunch" is singular) they go from B to A.

Who to believe??? It's enough to make anyone lose their composure. (Oh
but wait, there's left Kan extensions.)

Vaughan

PS?? How many covariant power set functors according to the Elephant???
Does every element of ?? get one?

On 09/14/17 8:58 AM, Peter Selinger wrote:
> Robert Pare wrote:
>> He said there may come a time when we have to consider covariant
>> functors as contravariant ones on the opposite category.
> This anecdote seems to have prompted a few posts about opposite
> categories, but I thought the point of the original anecdote was that
> Fred said that *covariant* functors should be considered as
> contravariant functors on the opposite category, i.e., that he
> considered contravariant functors to be the more fundamental concept.
> An interesting thought, and obviously tongue-in-cheek.
>
> -- Peter
>

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