# 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

## 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

## 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