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On weak maps between 2-groups
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We give an explicit handy (and cocycle-free) description of the groupoid of weak maps between two crossed-modules in terms of certain digrams of groups which we we call a {\em butterflies}. We define composition of butterflies and this way find a bicategory that is naturally biequivalent to the 2-category of pointed homotopy 2-types. We indicate how certain standard notions of 2-group theory (e.g., kernels, cokernels, extension of 2-groups, and so on) find a simple description in terms of butterflies. We also discuss braided and abelian butterflies.
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Higher symmetries and anomalies in quantum lattice systems
For 1d and 2d quantum lattice systems, this paper shows that anomaly indices are naturally viewed as the pullback of the Postnikov class of a 2-group or 3-group of local symmetries, so anomalies arise from mixing ordi...
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