An example of what Marcus is saying is that using the category definition of duality you can show that the dual space of the dual space is (is isomorphic to) the original space. That's easy to show without the added generality.
--- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Mon, Oct 25, 2021, 11:20 AM Frank Wimberly <wimber...@gmail.com> wrote: > I found this to be helpful. The dual space of a vector space must be an > instance of this category theory concept of dual. > > https://en.m.wikipedia.org/wiki/Dual_(category_theory) > > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Mon, Oct 25, 2021, 10:04 AM Marcus Daniels <mar...@snoutfarm.com> > wrote: > >> Could be. But isn’t it obvious that writing a CA in some imperative >> language requires less hand wringing? What is the payoff? So much of >> this stuff ends up coming across as “Look you can do the thing you already >> knew how to do!” What can I do that I couldn’t do before? >> >> >> >> *From:* Friam <friam-boun...@redfish.com> *On Behalf Of *Barry MacKichan >> *Sent:* Monday, October 25, 2021 8:52 AM >> *To:* The Friday Morning Applied Complexity Coffee Group < >> friam@redfish.com> >> *Subject:* Re: [FRIAM] stygmergy, CA's, and [biological] development >> >> >> >> Aha! I think the exercise here was to come up with a categorical >> statement. >> —Barry >> >> On 25 Oct 2021, at 10:19, Marcus Daniels wrote: >> >> It is hard to find the motivation to invest much in category theory when >> the practical considerations are left as an exercise to the reader. >> >> >> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - . >> FRIAM Applied Complexity Group listserv >> Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam >> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> archives: >> 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ >> 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >> >
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