#λ Category Theory Illustrated - Functors
https://abuseofnotation.github.io/category-theory-illustrated/06_functors/
"… What are functors …" #Functional #Programming #isomorphism
thanks https://lobste.rs/s/pjy2bo/category_theory_illustrated_functors
¹ https://mro.name/asuek9t

Isomorphism (Math)

https://en.wikipedia.org/wiki/Isomorphism

#Math #Isomorphism #Articles

In the Way of Inquiry • Formal Apology 7
• https://inquiryintoinquiry.com/2023/01/12/in-the-way-of-inquiry-formal-apology-2/

Explosional Recombinations

An eye to form provides a way to manage the wealth of material diversity by observing formal similarities among materially distinct domains. It allows the same formal answer to unify a host of concrete questions under a single roof, reducing the variety of topics requiring coverage.

#Peirce #Inquiry #InquiryIntoInquiry #InquiryDrivenSystems
#Abstraction #Form #Isomorphism #Combinatorics #Complexity

In the Way of Inquiry • Formal Apology 6
• https://inquiryintoinquiry.com/2023/01/12/in-the-way-of-inquiry-formal-apology-2/

Explosional Recombinations

Another obstacle to inquiry is posed by the combinatorial explosion of questions arising in complex cases. The embarrassment of riches found here is deceptively deadly to the ends of inquiry in the very measure it appears so productive at first.

#Peirce #Inquiry #InquiryIntoInquiry #InquiryDrivenSystems
#Abstraction #Form #Isomorphism #Combinatorics #Complexity

This makes me think a little about #isomorphism in other areas of mathematics. I feel like a lot of folks don't think too much about what the isomorphisms look like.

"All finite fields of the same size are isomorphic, QED", most people would say, and move on to the next question. "All vector spaces of the same dimension are isomorphic, QED", they continue.

Yes, but depending on how you represent your field or vector space, it will look very different!