Mathematical objects of a certain sophistication are frequently accompanied by higher homotopical structures: Maps between them might be connected by homotopies that witness the weak commutativity of diagrams, which might then be connected by higher homotopies expressing coherence conditions among these witnesses, which might then be connected by even higher homotopies ad infinitum. The natural habitat for such mathematical objects is not an ordinary 1-category but instead an ∞-category or, more precisely, an (∞, 1)-category,
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