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Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
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Equivalent parallel pair of $j$-morphisms
It means that between every two $j$-cells with the same domain and codomain ($j > n$), there is a $(j + 1)$-cell between them (which is necessarily an equivalence by the first condition of the definit …