On weak maps between 2-groups

Behrang Noohi

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On weak maps between 2-groups

Behrang Noohi

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Abstract

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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BibTeX RIS

Behrang Noohi. 2008-07-13. On weak maps between 2-groups. https://arxiv.org/abs/math/0506313

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