A deep dive into order theory from a category-theoretic perspective. Covers linear (total) orders, partial orders, and preorders, explaining the laws governing each (reflexivity, transitivity, antisymmetry, totality). Explores key concepts like joins, meets, lattices, distributive lattices, and Birkhoff's representation theorem with concrete examples including color mixing, number divisibility, and set inclusion. Concludes by showing that preorders are thin categories, and that joins and meets correspond to categorical coproducts and products respectively.
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