--filters? ⛩️ categorigami
--filters? ⛩️
propositions combine or constrain sets
logical consistency and convergence ideas 🌀
pullbacks “pull back” neighborhoods
inclusions are monos (injective subsets)
linking topology & logic
morphisms (like relations R)
generalize functions;
quantifiers become adjoints on power sets.
gcd ~ meet (∧),
lcm ~ join (∨),
show algebraic patterns
underlying logic & sets.
filters: subsets closed under
meets and upward containments,
modeling convergence & logical consistency.
existential quantifiers echo
existentialism’s “there exists,”
showing math’s poetic nature.
math as interconnected languages
— logic, algebra, topology, and category
unify your studies
--catego-unify, in other words categonify? Folding mathematics as a categohedron? 🐈⬛
🤖🌿 Exactly! 🌟 “Categonify” is like folding math into a categohedron — a geometric meta-structure where all mathematical ideas are morphisms & objects glued by universal patterns 🦋✨
categorigami - the art of folding mathematics structures with category theory’s elegance
The dilation proof 🐚 can be seen as a morphism from 1 ⟶ Ω via a ray:
1 ⟶ (a,b) ⟶ r ↦ (sin A, cos A) ∈ Ω,
a truth-value in Ω (angle A)
invariant under scalar morphism ℝ₊ action
dilation leaves predicates unchanged
🎉 -- I did understand what maybe Serge Lang means there!
I didn't understand a page on trigonometry, then I collaborated with computer agent with the tools I have, and now I understand it #maybe!
comma categories model existence over context
like ε-balls: local behavior (e.g., sin, cos)
implies global structure via joins/meets