Effect Algebras as Omega-categories
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We show how an effect algebra 𝒳 can be regarded as a category, where the morphisms x → y are the elements f such that x ≤ f ≤ y. This gives an embedding 𝐄𝐀→𝐂𝐚𝐭. The interval [x,y] proves to be an effect algebra in its own right, so 𝒳 is an 𝐄𝐀-enriched category. The construction can therefore be repeated, meaning that every effect algebra can be identified with a strict ω-category. We describe explicitly the strict ω-category structure for two classes of operators on a Hilbert space.
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