[[The following email is sent on behalf of posinavrayudu@gmail.com]] Dear All, Consider a category of objects (say, cats). Going by a naive understanding of the notion of category, every object of a category partakes in an essence/abstract general/theory that is characteristic of the category (cf. catness; whatever that might be). Doesn't it immediately follow from this commonplace understanding of category that morphisms of a category are necessarily natural transformations preserving the abstract essence characterizing the category (cf. playful cat ---> pensive cat). Of course, this is an informal paraphrasing of "Yoneda showed that maps in any category can be represented as natural transformations" (Lawvere & Schanuel, Conceptual Mathematics, p. 378). Isn't this reason enough to think of category theory as the theory of naturality? Happy Monday :) Thanking you, Yours truly, posina P.S. Given that all morphisms, beginning with functions between sets (https://conceptualmathematics.wordpress.com/2022/08/30/functions-are-natural-transformations/<https://conceptualmathematics.wordpress.com/2022/08/30/functions-are-natural-transformations>), can be construed as natural transformations, one added value of baptizing category theory as the theory of naturality is that it brings into figural salience for all see that the constrasting notion is unnatural (as in miracles) and not social or culture (since they too don't change willy-nilly). To be clear, highlighting natural is not intended to belittle the categorical nature of our everyday experience (Kandel et al., Principles of Neural Science, pp. 621-637). On Mon, Oct 23, 2023 at 11:10 AM JS Lemay <js.lemay@mq.edu.au> wrote:
Hello everyone!
Welcome to the new category theory mailing list.
Unfortunately, the old categories mailing list categories@mta.ca has gone permanently offline.
Bob Rosebrugh, the old mailing list's moderator, reached out to me and asked me to set up a new mailing list. So thank you for your patience while we were getting this new mailing list up and running. (Big thanks to Richard, Steve, and Macquarie's IT team for helping me with this!)
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