Tag Archives: algebra

Why bicontinuity is the right condition for topological equivalence (homeomorphism): if continuity of the inverse isn’t required, then a circle could be equivalent to a line (.99999 and 0 would be neighbours) — Minute 8 or so. Geometric construction (no … Continue reading

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Graphical Axioms from the nCatLab

If you don’t read the n-category café’s wiki project, you are missing out. Definition. A Frobenius algebra in a monoidal category is a quadruple (A,δ,ϵ,μ,η) such that (A,μ,η) is a monoid, (A,δ,ϵ) is a comonoid, and the Frobenius laws hold: (1⊗μ)∘(δ⊗1)=δ∘μ=(μ⊗1)∘(1⊗δ). In terms of string diagrams, this definition says: The first line here … Continue reading

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Ex Ante / Ex Post Conflicts

M. You live in a society where lovers choose whom to marry based on romance. So you don’t want to give up your right to choose a partner (or no partner at all). But if you actually lived under rules of … Continue reading

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Linear Transformations will take you on a Trip Comparable to that of Magical Mushroom Sauce, And Perhaps cause More Lasting Damage Long after I was supposed to “get it”, I finally came to understand matrices by looking at the above … Continue reading

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Superadditivity

“The whole is more than the sum of the parts” Who says scientists are reductionistic? Any superadditive system—due to complexity, interaction terms, valuation by an Lₚ norm with 0<p<1, or some other reason—adds up to more in total than the … Continue reading

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Ethnic Food as a Poset

I like Indonesian food better than Japanese food i ⪰ j, and I like Japanese food better than English food j ⪰ e. I also like French food better than English food f ⪰ e, but I see French food as so different … Continue reading

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Popularity

At my secondary school, the high-scoring wide receiver was more popular than the fat lineman. And the fat lineman was more popular than the team statistician. But you couldn’t really compare the wide receiver’s popularity to that of the actor … Continue reading

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