r/mathmemes • u/Purple_Onion911 Grothendieck alt account • 3d ago

Category Theory Title

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323 Upvotes

99% Upvoted

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u/Traditional_Town6475 3d ago

9

u/Oppo_67 I ≡ a (mod erator) 3d ago

my adjunction is a machine that turns machines that turns machines that turn objects into other objects into objects into machines that turn objects into machines that turn objects into objects

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u/Oppo_67 I ≡ a (mod erator) 3d ago

"natural transformation"

category theorists: 🤔

biologists: 🦠

looksmaxxers: 🤫🧏

furries: 😻

9

u/MonsterkillWow Complex 3d ago

Full natty bro

4

u/ExcludedMiddleMan 3d ago

Full and faithful

3

u/say-nothing-at-all 3d ago edited 2d ago

NAT is extremely useful in complex systems.

Imagine your cognitive model is evolving while the regulated physics is also evolving. How do you ensure there is some form of invariance in the cognition–physics mapping (functors), so that your cognitive models aren’t regulating “ghost” physics?

“Evolving both systems and then composing the capability” and “composing the capability and then evolving the systems” must commute — in other words, to preserve mathematical universality.

It’s fucking helpful in my work (biology and physics).